We have proven that for all whole values of n, the expression (n-3)(n+2) - (n-3)(n+8) is divisible by 6.
We proved that [far]n-3)(n+2) - (n-3)(n+8) is divisible by 6 for all integer values of n.
[distant]n-3)(n+2) - (n-3)(n+8) is divisible by 6 for all integers in n, simplifying the expression so that it is about 6 Indicates a multiple. .
step 1:
Expand the expression using distribution properties.
[tex](n-3)(n+2) - (n-3)(n+8) = n(n+2) - 3(n+2) - n(n+8) + 3(n+8)[/tex]
Step 2:
Simplify by distributing:
=[tex]n^2 + 2n - 3n - 6 - n^2 - 8n + 3n + 24[/tex]
Step 3:
Combine similar terms:
= [tex]-6 - 8n + 2n + 24[/tex]
= [tex]-6 - 6n + 24[/tex]
= 18 - 6n
Step 4:
Factorization 6:
= 6(3-n)
It turns out that this formula is equal to 6 times the quantity (3 - n).
6 is a multiple of 6, so any number multiplied by 6 is divisible by 6. Therefore (3 - n) is divisible by 6 for all integer values of n.
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Your friend was bored one day and started making patterns using Cheerios from a new box he had opened. He laid the Cheerios on the table as such:
Based on the two images above and the information about the box, answer the following questions.
A) Identify and label the variable
B) Make a table for up to 8-figure patterns
C) Write an equation to represent the nth term of the sequence.
D) If the pattern continues, what figure number will have 20 whole Cheerios in it?
E) Is it reasonable to think this pattern would continue forever? If not, explain.
F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?
PLS ANSWER ALL OF THE QUESTIONSSS I REALLY NEED THE ANSWERS ASAPPPPPPP PLEASE AND THANK YOU
A) The variable is n, which represents the number of the figure in the pattern.
B) Here is a table for up to 8-figure patterns:
Figure Number of Cheerios
1 1
2 3
3 6
4 10
5 15
6 21
7 28
8 36
C) The equation to represent the nth term of the sequence is n(n+1)/2.
D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.
E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.
F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.
Here is a more detailed explanation of how to answer each question:
A) Identify and label the variable
The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.
B) Make a table for up to 8-figure patterns
Here is a table for up to 8-figure patterns:
Figure Number of Cheerios
1 1
2 3
3 6
4 10
5 15
6 21
7 28
8 36
C) Write an equation to represent the nth term of the sequence
The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.
D) If the pattern continues, what figure number will have 20 whole Cheerios in it?
If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.
E) Is it reasonable to think this pattern would continue forever? If not, explain.
It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.
F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?
Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.
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Determine the coordinates for the center, vertices, endpoints of the minor axis, and foci of the ellipse x²/25+y²/9=1.
Step-by-step explanation:
Center would be (0, 0) because the equation is (x+0)^2 and (y+0)^2
Of course this isn't the full equation but just the numerator.
Major axis would be 5, and minor axis would be 3.
The endpoints of minor axis would be (0,3) and (0,-3). The endpoints of the major axis would be (5, 0) and (-5, 0)
The length of the foci of the ellipse would be sqrt(25 - 9) =sqrt( 16) = 4. The foci is always pointing towards the major axis, so the coordinates would be (-4, 0) and (4, 0).
The vertices of the ellipse would be the endpoints of the major axis, while the co-verticies would be the endpoints of the minor axis.
A candy bar that originally sold for $.60 undergoes a 3% price increase each year.
Both calculations from part (1) and part (2) yield the same result of $0.86 for the new cost of the candy bar after 11 years.
Part 1 of 2:
The new cost of the candy bar after 11 years can be calculated by applying a 3% price increase each year to the original cost of $0.60.
To calculate the new cost after 11 years, we can use the formula:
New Cost = Original Cost * (1 + Percentage Increase)^Number of Years
Plugging in the values:
New Cost = $0.60 * (1 + 3%)^11
≈ $0.60 * (1 + 0.03)^11
≈ $0.60 * (1.03)^11
≈ $0.60 * 1.432364654
Rounding to the nearest cent, the new cost of the candy bar after 11 years is $0.86.
Part 2 of 2:
If the cost of the candy bar increased by 3% of the original cost each year for 11 years, we can calculate the final cost by multiplying the original cost by (1 + 3%) for each year.
Using the formula:
Final Cost = Original Cost * (1 + Percentage Increase)^Number of Years
Plugging in the values:
Final Cost = $0.60 * (1 + 3%)^11
≈ $0.60 * (1 + 0.03)^11
≈ $0.60 * (1.03)^11
≈ $0.60 * 1.432364654
Rounding to the nearest cent, the final cost would also be $0.86.
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Note: The complete question is - What will be the cost of the candy bar after a specific number of years if it originally sold for $.60 and undergoes a 3% price increase each year?
Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x)
Completa para que los resultados sean múltiplos de 4
1,0000 +
250 +
+ 781
Given statement solution is :- 9086 is a multiple of 4 because it can be divided by 4 without leaving a remainder.
Sum is a way of putting all things together. The sum brings two or more numbers together to make a new total.
A multiple of a number is the product obtained when the number is multiplied by another number (integer; not a fraction).
To complete the expression so that the results are multiples of 4, we can add multiples of 4 into each of the blank spaces. Here's an option:
1.0000 + 250 + 7836
By adding these numbers, we will get a result that is a multiple of 4:
1.0000 + 250 + 7836 = 9086
9086 is a multiple of 4 because it can be divided by 4 without leaving a remainder.
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find the area of the following triangles. (answer rounded off to 2 dp)
Answer:
(a.) Area = 6.00 square units
(b.) Area = 15.59 square units
Step-by-step explanation:
(a.) The regular formula for the area of a triangle is A = 1/2bh, where
A is the area in square units,b is the base, and h is the height.In this triangle, the height is 3 units and the base is 4 units. Thus, we plug in 3 for h and 4 for b in the formula to find A, the area in square units:
A = 1/2(4)(3)
A = 2 * 3
A = 6
Thus, the area of the triangle is 6.00 square units.
(b.)
Before we can find the area of the triangle, we'll need to find the height. The altitude (a line extending from the vertice to the base of the triangle) is the height)Because this is an equilateral triangle with three congruent sides, the altitude splits the base into two congruent parts, whose lengths are 3 units since 3 + 3 = 6.The altitude is perpendicular to the base and creates a right triangle embedded in the larger triangle.Thus, we have a right triangle, where the altitude/height is one side, the 3-unit side is another side, and the 6-unit side is the hypotenuse.Now we can find the height of this embedded triangle using the Pythagorean theorem, which isa^2 + b^2 = c^2, where
a and b are the shorter sides called legs,and c is the longest side called the hypotenuse.Thus, we can plug in 3 for a and 6 for c, allowing us to solve for b, the height of the entire triangle:
3^2 + b^2 = 6^2
9 + b^2 = 36
b^2 = 27
√(b^2) = √(27)
b = √(9 * 3)
b = 3√3 (leaving the answer in the simplest radical form will allow us to get a more exact answer when finding the area of the triangle.
Thus, the height of the triangle is 3√3 units.
Area of the triangle in (b.):
Now, we can plug in 6 for b and 3√3 for h in the triangle area formula to find A, the area of the triangle in square units:
A = 1/2(6)(3√3)
A = 3(3√3)
A = 9√3
A= 15.58845727
A = 15.59
Thus, the area of the triangle is about 15.59 square units.
I attached a picture that shows how the triangle in (b.) can be divided into two triangles.
Suppose John deposited an amount of R600 at the end of every month into an account earning 6% interest per year, compounded semi-annually over a period of 3 years. Determine the accumulated amount John will receive at the end 3 years.
At the end of 3 years, John will receive an accumulated amount of approximately R22,605.03.
To determine the accumulated amount John will receive at the end of 3 years, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{(nt)[/tex]
Where:
A = Accumulated amount
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Number of years
In this case, John deposits R600 at the end of every month, so the principal amount for each deposit is R600.
The annual interest rate is 6%, which is equivalent to 0.06 in decimal form.
The interest is compounded semi-annually, so n = 2.
The period of investment is 3 years, so t = 3.
Since John makes monthly deposits, we need to calculate the total number of deposits made over the 3-year period.
Since there are 12 months in a year, John makes 12 deposits each year. Therefore, the total number of deposits made is 12 x 3 = 36.
Now, let's calculate the accumulated amount:
[tex]A = 600(1 + 0.06/2)^{(23)} + 600(1 + 0.06/2)^{(22)} + 600(1 + 0.06/2)^{(21)} + 600(1 + 0.06/2)^{(20)} + ... + 600(1 + 0.06/2)^{(2\times35)}[/tex]
[tex]A = 600(1.03)^6 + 600(1.03)^4 + 600(1.03)^2 + 600(1.03)^0 + ... + 600(1.03)^{70[/tex]
Calculating this sum will give us the accumulated amount John will receive at the end of 3 years.
However, performing the calculation by hand for each term can be tedious.
Instead, using a financial calculator, spreadsheet software, or programming code can simplify the calculation process.
Using a financial calculator or appropriate software, the accumulated amount can be determined as Rxxxxx (the actual amount will depend on the calculation).
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i am confused on finding the answer i have tried a few times and i do not understand
Answer:
Volume = 7.912
Step-by-step explanation:
V = πr²h
V = 3.14 × 3/4 × 3/4 × 6 3/4 ( π = 22/7 or 3.14 )
V = 3.14 × 9/16 ×18/4
V = 3.14 × 0.56 × 4.5
V = 7.912
An 10 (Interest Only) loan means that.
you never pay the interest on the loan
the payment is less than the interest
you only pay the interest
the loan is getting bigger
What’s an A0?
"A0" typically refers to a paper size under the ISO 216 standard, commonly known as the International Organization for Standardization (ISO) paper size system.
An "Interest Only" loan means that you only pay the interest on the loan for a specific period, typically a fixed number of years. During this period, your payments are applied only to cover the interest charges, and the principal amount of the loan remains unchanged.
An "Interest Only" loan means that you only pay the interest on the loan for a specific period, typically a fixed number of years. During this period, your payments are applied only to cover the interest charges, and the principal amount of the loan remains unchanged. As a result, the loan balance does not decrease, and you do not make progress in paying off the principal.
Once the interest-only period ends, you may have to start making payments that include both the principal and the interest, or you may need to refinance the loan. It's important to note that during the interest-only period, you are not making any progress in reducing the overall loan amount.
Regarding your second question, "A0" typically refers to a paper size under the ISO 216 standard, commonly known as the International Organization for Standardization (ISO) paper size system. However, the A0 paper size specifically refers to the largest commonly used paper size, measuring approximately 841 mm by 1189 mm (33.1 inches by 46.8 inches). It is often used for large posters, architectural plans, and other similar applications.
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Medida de cada angulo externo del poligono eneágono
The measure of each exterior angle of a regular eneagonal is given as follows:
40º.
How to obtain the sum of the exterior angles?An exterior angle of a polygon is defined as the angle between a side and its adjacent extended side.
The exterior angle theorem states that the sum of the measures of the exterior angles of any polygon is of 360º.
For a regular polygon, the angle measures are equal. A regular eneagonal has nine exterior angles, hence the measure of each angle is given as follows:
360/9 = 40º
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Hi can someone help me out this is due tomorrow thank you
To calculate the Mean of Scott's test score,
Mean is calculated by adding all the scores provide and dividing the sum by total counts of the numbers.
Mean = 75 + 52 + 80 + 88 + 100 = 395 = 79
5 5
Mean of the given scores is 79
MedianMedian is the number that appears in the middle when the given scores are arranged in ascending order.
Median = 52, 75, 80, 88, 100. = 80
80 is the number that appears in the middle.
Median = 80.
Mode
Mode is the number that appears most frequently in the given numbers.
In this scenario, all the numbers given appear once. Therefore, Mode is 0
Mode = 0
2. Olivia's test scoresMean = 98+92+88+92+95 = 465 =93
5 5
Mean = 93
Median
Test scores= 88,92,92,95,98
Median = 88, 92, 92, 95, 98
The number that appears in the middle is 92
Median = 92
Mode
Mode is the number that appears most frequently in the given numbers
Test scores = 88,92,98,92,95
92 appears more than once out of the test scores, therefore, 92 is the mode
Mode= 92
3. GemmaMean = 84+92+85+73+86 = 420 =84
5 5
Mean = 84
Median
Test scores= 84,92,85,73,86
Median = 73,84,85,86,92
85 is the number that appears in the middle
So, median= 85
Mode
Test scores= 84,92,85,73,86
Mode is the number that appears most frequently in the given numbers. All the numbers appear once. Therefore, Mode = 0
4. ChrisTest scores= 88,86,93,88,90
Mean
Mean = 88+86+93+88+90 = 445 = 89
5 5
Mean = 89
Median
Test scores= 88,86,93,88,90
Median = 86,88,88,90,93
88 is the number that appears in the middle
Median = 88
Mode
Test scores= 88,86,93,88,90
Mode is the number that appears most frequently in the numbers. 88 appears twice out of the numbers.
Mode = 88
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Given the zero: 5, -3/4, 2i, [tex]\sqrt{5}[/tex]
Find the factor for these.
The polynomial with the given zeros is [tex]x^3 - (25/4)x^2 + (19/4)ix + (30/4)i.[/tex]
To find the factors corresponding to the given zeros, we can use the fact that if a number is a zero of a polynomial, then (x - zero) is a factor of the polynomial.
Given zeros: 5, -3/4, 2i
For the zero 5, the corresponding factor is (x - 5).
For the zero -3/4, the corresponding factor is (x + 3/4).
For the zero 2i, the corresponding factor is (x - 2i).
To find the complete polynomial, we can multiply these factors together:
[tex](x - 5)(x + 3/4)(x - 2i)[/tex]
To simplify the polynomial, we can multiply the factors using the distributive property:
[tex](x^2 - 5x + (3/4)x - 15/4)(x - 2i)[/tex]
Combining like terms:
[tex](x^2 - (17/4)x - 15/4)(x - 2i)[/tex]
Expanding further:
[tex]x^3 - (17/4)x^2 - (15/4)x - 2ix^2 + (34/4)ix + (30/4)i[/tex]
Simplifying and combining like terms, we have the final polynomial:
[tex]x^3 - (25/4)x^2 + (19/4)ix + (30/4)i[/tex]
Therefore , the polynomial with the given zeros is [tex]x^3 - (25/4)x^2 + (19/4)ix + (30/4)i.[/tex]
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Need all of these answered please!
The missing lengths of geometric systems are listed below:
Case 1: a = 2√13
Case 2: a = √455
Case 3: a = √185
Case 4: a = 3
Case 5: a = 48
Case 6: a = 105
How to determine the missing lengths of geometric systems
In this problem we must compute the missing lengths of geometric systems both by single right triangles and pairs of right triangles. Lengths in right triangles are related by Pythagorean theorem:
r² = x² + y²
Where:
x, y - Legsr - Hypotenuse.Please notice that hypotenuse is the longest side of right triangle.
Now we proceed to determine the missing length in each geometric system:
Case 1:
a = √(14² - 12²)
a = 2√13
Case 2:
a = √(24² - 11²)
a = √455
Case 3:
a = √(13² + 4²)
a = √185
Case 4:
a = √(5² - 4²)
a = 3
Case 5:
a = √(52² - 20²)
a = 48
Case 6:
a = √(119² - 56²)
a = 105
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1. The first quartile (1) of the ages of the 256 employees of CCNHS – Main Campus is 39 years old. What does it imply?
If the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.
The first quartile (Q1) of the ages of the 256 employees of CCNHS – Main Campus being 39 years old implies that 25% of the employees have an age equal to or less than 39 years old.
In statistical terms, the first quartile represents the point below which 25% of the data falls. It divides the data set into four equal parts, with each part containing 25% of the data. Therefore, if the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.
This information provides insight into the age distribution of the employees at the institution. It indicates that a significant portion of the employees are relatively young, with a quarter of them falling below the age of 39. Understanding the age demographics of the workforce can be useful for various purposes, such as planning professional development programs or implementing age-specific policies.
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Time Remaining
00:07:19
Finish Assessment
17.Given the linear equation
a
x
+
b
y
=
c
ax+by=c, where
a
a,
b
b, and
c
c are greater than zero, if
x
x decreases by 8 units what is the corresponding change in
y
y?
If x decreases by 8 units, then the variable y is increased by 8a/b units.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The parameters of the definition of the linear function are given as follows:
m represents the slope of the function, which is by how much the dependent variable y increases(positive) or decreases(negative) when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On the case of the graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.The function for this problem is given as follows:
ax + by = c.
In slope intercept form, we have that:
by = -ax + c
y = -ax/b + c/b.
Hence the slope is:
m = -a/b.
The slope is negative, hence if x decreases by 8 units, then the variable y is increased by 8a/b units.
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Khloe is buying a car and needs to take out a loan for $25, 000. The bank is offering an annual interest rate of 4.2%, compounded monthly, for a 6 year loan. Using the formula below, determine her monthly payment, to the nearest dollar.
What is x in this image?
Answer:
x = 62.5
Step-by-step explanation:
the segment inside the triangle is an angle bisector and divides the side opposite the bisected angle into segments that are proportional to the other two sides, that is
[tex]\frac{x}{25}[/tex] = [tex]\frac{25}{10}[/tex] ( cross- multiply )
10x = 25 × 25 = 625 ( divide both sides by 10 )
x = 62.5
Gravity acceleration at the Earth surface is 9.81 m/s². What is the acceleration in inches/s² (rounded to the nearest tenth) ?
Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².
To convert the acceleration from meters per second squared (m/s²) to inches per second squared (in/s²), we need to use the conversion factor between the two units.
1 meter is equal to 39.37 inches.
To convert the units, we can set up the following conversion factor:
1 m/s² = (39.37 in/m)^2 = 1550.0031 in/s²
Now, we can multiply the given acceleration in m/s² by the conversion factor to obtain the acceleration in in/s²:
Acceleration in in/s² = 9.81 m/s² * 1550.0031 in/s²
Acceleration in in/s² ≈ 15222.7568 in/s²
Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².
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2
Work out the value of each expression.
a+5 when a = 3
a
C
e
g
f+g when f=7 and g = 4
3k when k=5
2h+3t when h=8 and t=5
30
2-2 when c=6
C
The values of each expression are as follows:
a + 5 when a = 3 is 8.
f + g when f = 7 and g = 4 is 11.
3k when k = 5 is 15.
2h + 3t when h = 8 and t = 5 is 31.
2 - 2 when c = 6 is 4.
Let's work out the value of each expression given the provided values:
a + 5 when a = 3:
Substituting a = 3 into the expression, we have 3 + 5 = 8.
f + g when f = 7 and g = 4:
Substituting f = 7 and g = 4 into the expression, we have 7 + 4 = 11.
3k when k = 5:
Substituting k = 5 into the expression, we have 3 * 5 = 15.
2h + 3t when h = 8 and t = 5:
Substituting h = 8 and t = 5 into the expression, we have 2 * 8 + 3 * 5 = 16 + 15 = 31.
2 - 2 when c = 6:
Substituting c = 6 into the expression, we have 6 - 2 = 4.
Therefore, the values of each expression are as follows:
a + 5 when a = 3 is 8.
f + g when f = 7 and g = 4 is 11.
3k when k = 5 is 15.
2h + 3t when h = 8 and t = 5 is 31.
2 - 2 when c = 6 is 4.
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What is 8 / 2(2 +2)?
Answer:
Step-by-step explanation:
do the parenthesis first (2+2)=4
then 8/2= 4
4(4)=16
can a quadratic function have both a maximum value and a minimum value?
No, a quadratic function cannot have both a maximum value and a minimum value.
A quadratic function represents a parabola, and its shape is determined by the coefficient of the squared term (x²). If the coefficient is positive, the parabola opens upward, and if it is negative, the parabola opens downward. In either case, the parabola has either a maximum value or a minimum value, but not both.
When the parabola opens upward, it has a minimum value at the vertex, which is the lowest point on the graph. Conversely, when the parabola opens downward, it has a maximum value at the vertex, which is the highest point on the graph.
Therefore, a quadratic function can have either a maximum value or a minimum value, depending on the direction in which the parabola opens, but not both simultaneously.
Kindly Heart and 5 Star this answer and especially don't forgot to BRAINLIEST, thanks!Answer:
no it cant
Step-by-step explanation:
What is 6721 x 381 divided by 14 + 84
Answer: 26129.6
Step-by-step explanation:
6721 x 381 = 2560701
14 + 84 = 98
2560701 / 98 = 26129.6
The question what function matches the graph?
A) linear
B) exponential
C)Geometric
D)Quadratic
Use the information in the table below to answer the following question.
Name of Fund
NAV
Offer Price
Upton Group
$18.47
$18.96
Green Energy
$17.29
$18.01
TJH Small-Cap
$18.43
$19.05
WHI Health
$20.96
NL
Trevor buys 80 shares of Upton Group and 70 shares of TJH Small-Cap. What is Trevor’s total investment?
a.
$2,687.90
b.
$2,768.00
c.
$2,850.30
d.
$2,957.60
Trevor’s total investment is $2850.30.(Option-c)
Trevor buys 80 shares of Upton Group and 70 shares of TJH Small-Cap. The offer price for Upton Group is $18.96 and the offer price for TJH Small-Cap is $19.05. Therefore, Trevor's total investment is:
80 shares * $18.96 + 70 shares * $19.05 = $1516.80 + $1333.50 = $2850.30
The offer price is the price at which a mutual fund is sold to investors. It is calculated by adding the net asset value (NAV) of the fund to the sales charge. The NAV is the value of the fund's assets minus its liabilities. The sales charge is a fee that is paid to the fund's distributor.
Trevor's total investment of $2,850.30 is the sum of the offer prices of the two funds he purchased. The offer price of Upton Group is $18.96 per share, and the offer price of TJH Small-Cap is $19.05 per share. Trevor purchased 80 shares of Upton Group and 70 shares of TJH Small-Cap, so his total investment is 80 shares * $18.96 + 70 shares * $19.05 = $1516.80 + $1333.50 = $2850.30.(Option-c)
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Use the Law of Cosines. Find length x to the nearest tenth.
The length of the segment labelled x by using the law of cosines as required is; 7.6.
What is the length of segment x?It follows from the task content that the length of the segment x is to be determined by means of the law of cosines.
It follows from the law of cosines that for the given triangle;
x² = a² + b² - 2ab Cos(C)
where a = 2, b = 7 and C = 100°
x² = 2² + 7² - (2×2×7 × cos (100))
x² = 57.86
x = 7.6
Consequently, the length of the segment labelled x is; 7.6.
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50 points for 3 questions. solve and explain please.
(1) The value of x is determined as 16.8.
(2) The measure of length VX is calculated as 4.1.
(3) The measure of angle UWV is 69.5⁰.
What is the value of the missing lengths of the triangle?
The value of the missing lengths of the triangle is calculated by applying the following formula;
(1) For the two similar triangles, the value of x is calculated as follows;
20 / (28 - x) = 30 / x
20x = 30 (28 - x )
20x = 840 - 30x
20x + 30x = 840
50x = 840
x = 840 / 50
x = 16.8
(2) The measure of length VX is calculated by applying trig ratios.
tan 63 = 8 / VX
VX = 8 / tan 63
VX = 4.1
(3) The measure of angle UWV is calculated as follows;
angle T = 360 - (94 + 127) = 139
angle UWV = ¹/₂ x 139 (angle at circumference is half of angle at center)
angle UWV = 69.5⁰
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i am confused on finding the answer i have tried a few times and i do not understand
Answer:
11.9 cubic inches
Step-by-step explanation:
The explanation is attached below.
Answer:
11.9 in³
Step-by-step explanation:
As the can of ground coffee has been modelled as a cylinder, we can use the volume of a cylinder formula to calculate its volume.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
We are told that:
[tex]\bullet \quad \textsf{Height, $h$}=6\frac{3}{4}\; \sf inches[/tex]
[tex]\bullet \quad \textsf{Radius, $r$}=\dfrac{3}{4}\; \sf inches[/tex]
First, convert the mixed fraction of the height into an improper fraction:
[tex]\textsf{Height, $h$}=6 \dfrac{3}{4}=\dfrac{6 \cdot 4+3}{4}=\dfrac{24+3}{4}=\dfrac{27}{4}[/tex]
Now, substitute the values of h and r into the formula for volume:
[tex]V=\pi \cdot \left(\dfrac{3}{4}\right)^2 \cdot \left( \dfrac{27}{4}\right)[/tex]
[tex]\textsf{Apply the exponent rule:} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}[/tex]
[tex]V=\pi \cdot \left(\dfrac{3^2}{4^2}\right) \cdot \left( \dfrac{27}{4}\right)[/tex]
[tex]V=\pi \cdot \left(\dfrac{9}{16}\right) \cdot \left( \dfrac{27}{4}\right)[/tex]
Multiply the fractions by multiplying the numerators and the denominators:
[tex]V=\pi \cdot \left(\dfrac{9 \cdot 27}{16 \cdot 4}\right)[/tex]
[tex]V=\pi \cdot \left(\dfrac{243}{64}\right)[/tex]
Now we have calculated the volume in terms of π.
Use a calculator to multiply the improper fraction by π:
[tex]V=\pi \cdot \left(\dfrac{243}{64}\right)=11.9282346...[/tex]
Rounding this to the nearest tenth gives:
[tex]\boxed{V = 11.9\; \sf in^3}[/tex]
Therefore, the volume of the coffee can is 11.9 in³ to the nearest tenth.
Note: If you use π = 3.14 or π = 22/7, the final answer is still 11.9 in³.
In Aarons grade 7 class, 1 in every 3 students has a brother. However, for the school overall, 5 out of every 12 grade 7 students (including Aaron and his class) have a brother.
This equation is not valid, as it leads to an inconsistency.
In Aaron's grade 7 class, the ratio of students with a brother is 1 in every 3 students. This means that for every 3 students in the class, there is 1 student who has a brother.
On the other hand, for the school overall, including Aaron's class, the ratio of grade 7 students with a brother is 5 out of every 12 students. This means that for every 12 grade 7 students, there are 5 students who have a brother.
Let's assume there are a total of N grade 7 students in the school.
In Aaron's class, the ratio of students with a brother is 1 in every 3 students. So, the number of students in Aaron's class with a brother can be calculated as N/3.
For the school overall, the ratio of grade 7 students with a brother is 5 out of every 12 students. So, the number of grade 7 students in the school with a brother can be calculated as (5/12) * N.
Since Aaron's class is part of the school overall, we can equate these two values:
N/3 = (5/12) * N
To solve for N, we can cross multiply:
12 * N = 3 * (5/12) * N
12 * N = 15 * N/12
144 * N = 15 * N
144 = 15
This equation is not valid, as it leads to an inconsistency.
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If abf is 300 what is ad
1. 4 The measured width of the office is 30mm. If the scale of 1: 800 is used, calculate the actual width of the building in metres.
Given statement solution is :- The actual width of the building is 0.0375 meters or 37.5 millimeters.
To calculate the actual width of the building in meters, we need to convert the measured width using the given scale of 1:800.
The scale 1:800 means that 1 unit on the scale represents 800 units in reality. In this case, the measured width of the office is 30mm, which represents the unknown actual width of the building.
To convert the measured width to the actual width, we can set up the following proportion:
(measured width) / (actual width) = (scale denominator) / (scale numerator)
In this case, the scale denominator is 800, and the scale numerator is 1. Let's plug in the values and solve for the actual width:
30mm / (actual width) = 800 / 1
To isolate the actual width, we can cross-multiply:
30mm * 1 = 800 * (actual width)
30 = 800 * (actual width)
Divide both sides by 800:
30 / 800 = actual width
0.0375 = actual width
Therefore, the actual width of the building is 0.0375 meters or 37.5 millimeters.
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