The length of the third side of the right triangular flower bed is 10 feet.
A right-angled triangle is a triangle with one of its interior angles equal to 90°. The side opposite to the right angle is the largest side and is referred to as the hypotenuse. Hypotenuse is always greater than any of the other two sides.
If two of the sides of the flower bed are 7 feet long each, then these are the sides adjacent to the right angle. We are to find the length of the third side, which is the hypotenuse, using the Pythagorean theorem.
Pythagorean Theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the two other sides.
c^2 = a^2 + b^2
where a and b are the adjacent sides to the right angle
c is the hypotenuse
c^2 = 7^2 + 7^2
c^2 = 49 + 49
c^2 = 94
c = 9.899
Hence, he length of the third side of the right-angled triangular flower bed is 10 feet.
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Find the sum of each finite series. Σ⁹ n=1 (-1)ⁿ . . . . 2
The sum of the given finite series is -1
The given series is:
[tex]\sum\limits^9_{n=1} {(-1)^{n}}[/tex]
The summation notation tell us that we need to add each term (-1)ⁿ as n moves from 1 to 9.
Let us expand this summation notation:
n = 1 ⇒ a(1) = (-1)¹ = -1
n = 2 ⇒ a(2) = (-1)² = 1
n = 3 ⇒ a(3) = (-1)³ = -1
We can continue to expand until n = 9, but we can see the pattern. The series can be written as:
[tex]\sum\limits^9_{n=1} {(-1)^{n}}=-1+1-1+1...-1[/tex]
We can see that a(1) and a(2) are cancelled out to each other. This applies to each pair of consecutive odd and even terms. Each term is cancelled out except a(9). Therefore:
[tex]\sum\limits^9_{n=1} {(-1)^{n}}=-1+1-1+1...-1=-1[/tex]
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State the property that justifies each statement.
If X Y+20=Y W and X Y+20=D T , then Y W=D T .
The characteristic that justifies each assertion Property of substitution
Briefing:The substitution property asserts that if a=b, then one can of replacing b in quite an expression or equation.
X Y+20=Y W and X Y+20=D T
then Y W=D T
What is the Substitution Property?The replacement property of equality states that "If a variable x is equal towards another variable y, then x may be substituted in place of y in whatsoever equation/expression and y can indeed be substituted throughout the place of x in any equation/expression."
Why is substitution significant in mathematics?Substitution connects many aspects of mathematics and hence aids in viewing mathematics as an entire discipline.
How do they solve through substitution?Three phases are involved in the substitution method: Solve this equation for a single of the variables. Substitute (plug-inin) this equation into a different equation and solve. Replace the value inside this original equation to obtain the equivalent variable.
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Charlyne deposited $3400 into a savings account that has an annual simple interest rate of 0.2%. Find the amount in the savings account after each number of years.
2 years $
5 years $
8 years $
The amount in the savings account after 2 years, 5 years and 8 years is respectively $13.6, $34, $54.4.
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't really compound, therefore the creditor only has to pay more interest on the principal sum and the borrower never has to pay interest on the interest that has already accrued.
Principle=3400
Rate of interest=0.2
Time period=2, 5 and 8 years
To calculate simple interest I= PRT/100
=> To find the amount in the savings account after 2 years
=(3400×0.2×2)/100
=13.6
So the amount in the savings account after 2 years is $13.6.
=> To find the amount in the savings account after 5 years
=(3400×0.2×5)/100
=34
Therefore the amount in the savings account after 5 years is $34.
=> To find the amount in the savings account after 8 years
=(3400×0.2×8)/100
=54.4
Hence the amount in the savings account after 8 years is $54.4.
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Answer:
2 years: 3413.60 or 3,413.60
5 years: 3434, 3,434.00, 3,434, or 3434.00
8 years: 3454.40 or 3,454.40
(the other persons is wrong)
Suppose a is a 57 matrix. How many pivot columns must a have if its columns span ? why?.
There must be pivot columns in the matrix. "A has a pivot place in every row" and "A's columns span an R5" seem to be logically equivalent.
What is defined as pivot columns?When a matrix has been in row-echelon form, the first nonzero entry in each row is referred to as a pivot, as well as the columns wherein pivots appear are referred to as pivot columns.
If two matrices in row-echelon form seem to be row-equivalent, their pivots are in the exact same locations.In the question asked, if the column of the 5x7 matrix is equal to R5, and the A span is equal to R5, and the value of A has a pivot for each row, then the position of each pivot in the separate columns of A has the 5 pivot columns.The matrix must contain pivot columns. "A has a pivot position in each row" & "A's columns span an R5" appear rationally equivalent.
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The correct question is-
Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R⁵? Why?
What’s the answers to b,c and d for 20 points.
The expression can be simplified as follows:
a. (-4)(-2) -6(2 - 5) = 26
b. 12.7 - 18.5 + 15 + 6.3 - 1 + 28.5 = 43
c. 23 - (17 - 3.4)² + 6 = -155.96
How to solve an expression using PEMDAS rule?The expressions can be solved using PEMDAS rule,
P = Parenthesis
E = Exponential
M = Multiplication
D = division
A = addition
S = Subtraction
Hence,
a.
(-4)(-2) -6(2 - 5) = (-4)(-2) - 6(-3) = 8 + 18 = 26
b.
12.7 - 18.5 + 15 + 6.3 - 1 + 28.5 = -5.8 + 15 + 6.3 - 1 + 28.5 = 9.2 + 6.3 - 1 + 28.5 = 15.5 - 1 + 28.5 = 14.5 + 28.5 = 43
c.
23 - (17 - 3.4)² + 6 = 23 - (13.6)² + 6 = 23 - 184.96 + 6 = -161.96 + 6 = -155.96
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Use the Distance Formula to find the distance between the pair of points.
O(-12,0), P(-8,3)
Using the distance formula, the distance between the pair of points O(-12,0) and P(-8,3) is 5 units
Given,
The points = O(-12,0) and P(-8,3)
We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex]
Substitute the values in the equation
The distance [tex]=\sqrt{(-8--12)^{2}+(3-0)^{2} }[/tex]
[tex]=\sqrt{4^{2}+3^{2} } \\=\sqrt{16+9} \\=\sqrt{25}[/tex]
= 5 units
Hence, using the distance formula, the distance between the pair of points O(-12,0) and P(-8,3) is 5 units
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Three cards are selected from a standard deck of 52 cards. What is the probability that all three cards are diamonds if neither the first nor the second card is replaced?
The probability that all three cards are diamonds if neither the first nor the second card is replaced: 0.0132
In this question,
We have been given a standard deck of 52 cards.
Three cards are selected from a standard deck of 52 cards.
Sample space n(S) = 52
We need to find the probability that all three cards are diamonds if neither the first nor the second card is replaced.
We know that, in a standard deck of 52 cards, there are 13 diamond cards.
The probability that the first card is diamond,
P1 = 13/52
The card is not replaced, so the total number of cards in a standard deck = 51
And the number of diamonds = 12
Now the probability that second card would be diamond,
P2 = 12/51
Similarly the probability that the third card is diamond,
P3 = 11/50
So, the probability that all three cards are diamonds if neither the first nor the second card is replaced:
⇒ P = P1 × P2 × P3
⇒ P = 13/52 × 12/51 × 11/50
⇒ P = 0.25 × 0.24 × 0.22
⇒ P = 0.0132
Therefore, the probability that all three cards are diamonds if neither the first nor the second card is replaced: 0.0132
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Write an algebraic expression that models each word phrase.
the quotient of the sum of 2 and a number b , and 3
The algebraic expression of the word phrase "The quotient of the sum of 2 and a number b and 3" is [tex]\frac{2+b}{3}[/tex]
Given
The word phrase
"The quotient of the sum of 2 and a number b and 3"
Sum off 2 and a number b = 2+b
Then the quotient of the sum of 2 and a number b and 3 = [tex]\frac{2+b}{3}[/tex]
Hence ,the algebraic expression of the word phrase "The quotient of the sum of 2 and a number b and 3" is [tex]\frac{2+b}{3}[/tex]
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Determine whether each infinite geometric series converges or diverges. If the series converges, state the sum. 150+30+6+ . . .
The given infinite geometric series 150+30+6+ . . . is convergent and the sum is 187.5
The given geometric series is:
150 + 30 + 6 + . . .
The common ratio (r) of a geometric series is given by:
r = a(n) / a(n - 1)
Notice that in the given series:
a(1) = 150
a(2) = 30
a(3) = 6
Hence, the common ratio is
r = a(2) / a(1) = 30/150 = 1/5
An infinite geometric series is convergent if 0 < | r | < 1.
Since r = 1/5, then the series is convergent and the sum exists.
Use the sum formula:
S = a(1) / (1 - r)
Substitute a(1) = 150 and r = 1/5 into the formula:
S = 150 / (1 - 1/5)
= 150 / (4/5)
= 187.5
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Find the center and the radius of each circle. (x+5)²+y²=18
The equation of the circle (x + 5)^2 + y^2 = 18 has a radius of 3√2 and a center located at (-5 , 0).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x + 5)^2 + y^2 = 18, is in standard form, then
h = -5
k = 0
r = 3√2
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Which describes myra’s distance as time increases? increasing decreasing zero constant
Myra's distance is increasing as time increases.
Given table showing the time (in minutes) and distance (in miles) :
Time (in minutes) Distance (in miles)
0 0.0
2 0.4
4 0.8
6 1.2
8 1.6
As we can see from the table, when there is an increase of 2 minutes in time, the distance is increasing by 0.4 miles.
So the distance covered by Myra is increasing with increase in time.
The question is incomplete. Find the complete question below:
The table shows the total distance that Myra runs over different time periods. A 2-column table with 5 rows titled Time and Distance Ran by Myra. The first column is labeled Time (minutes) with entries 0, 2, 4, 6, 8. The second column is labeled Distance (miles) with entries 0. 0, 0. 4, 0. 8, 1. 2, 1. 6. Which describes Myra's distance as time increases? increasing decreasing zero constant.
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help please i’ll name you brainliest
Answer: 6 and 27
Step-by-step explanation:
Answer:
Step-by-step explanation:
4x+8= 4(x+2) and that should be the answer if not then i don't know what to do
find the value of x if RS bisects AB and RS = 36
The value of the variable 'x' shown in th the geometrical figure is equal to 2cm
What is line bisector?
A line bisector divides the line into two equal parts. For a line of length ' L ', the bisector divides the line into two equal parts of length L/2 each.
Given is a geometrical figure in which RS is bisector of AB at point T and RS = 36.
RS bisects AB at point T. Therefore, we can say that T is the mid-point of AB. So, we can write -
AT = TB
25 - 3x = 2y - 5
- 3x - 2y = - 5 - 25
-(3x + 2y) = - 30
3x + 2y = 30 ...[1]
RS = 36
RT + TS = 36
2y - 6 + 18 = 36
2y + 12 = 36
2y = 24
y = 12
Substitute y = 12 in [1], we get -
3x + 2 x 12 = 30
3x + 24 = 30
3x = 6
x = 2
Therefore, the value of x = 2
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Pleaseeee Helppp
mx=n+p for x
Answer:
n – p
x= –––––
m
Hope that helps! Have a good day :)
V=4πct + 2πc squared solve for t
Step-by-step explanation:
Hope the pictures will help you
You are driving to a vacation spot with your family that is 1500 miles away. Including rest stops, you take 42 hours to get the the vacation spot. You drove on an average speed of 42 miles per hour. How many hours were you NOT driving? Please include an algebraic equation.
Answer:
Below in bold.
Step-by-step explanation:
The time you were driving = distance / average speed
= 1500/42
= 35.714 hours.
Required equation is
t = 42 - d/s where t = time not driving, d = distance and s = average speed
Time not driving :
t = 42 - 35.714
= 6.286 hours
That is about 6 hours 17 minutes.
Zahraa is calculating the quotient of 54,379÷289. She set up the long division with the numbers in the correct places. Zahraa says the first division to perform is determining how many whole times 289 divides into 5,437. Is this correct? Explain.
It should be noted that Zahraa saying that the first division to perform is determining how many whole times 289 divides into 5,437 is incorrect.
How to calculate the value?It should be noted that based on the information, Zahraa is calculating the quotient of 54,379÷289 and she set up the long division with the numbers in the correct places.
She said that first division to perform is determining how many whole times 289 divides into 5,437. This is incorrect.
It should be noted that the first thing to do is to find the number of times that 28 will go in 54 and then bring the remainder down and solve till she gets the final value.
In this case, 54,379÷289 will be 188 47/289
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Shawna works for a company that makes frozen pizzas. She cooked a sample of pizzas in
different ovens and let them cool in different rooms. She noticed an exponential relationship
between cooling times and pizza temperatures after cooking.
Shawna took the base 10 logarithm for the temperatures only, and she noticed a linear
relationship between the cooling times and the transformed temperatures.
Here's the least-squares regression equation for the transformed data, where "time"
represents minutes spent cooling, and "temp" is the pizza's temperature in degrees Celsius.
log(temp) = 2.390 -0.004(time)
According to this model, what is the predicted temperature of a pizza that cools for 20
minutes?
You may round your answer to the nearest whole degree.
Answer:
204 °C
Step-by-step explanation:
You want the predicted temperature of a pizza that has cooled for 20 minutes, as predicted by the formula ...
log(temp) = 2.39 -0.004·time
where temp is in degrees Celsius, and time is in minutes.
Evaluating the formulaUsing time = 20 in the formula, we find ...
log(temp) = 2.39 - 0.004·20 = 2.39 -0.08 = 2.31
Taking the antilog, we find the temperature to be ...
temp = 10^2.31 ≈ 204.2 . . . . . degrees C
The predicted temperature of the pizza is 204 °C.
Solve each equation. Check your answers. x/2 + x/3 =15
The solution of the given equation x/2 + x/3 = 15 is x = 18
In this question,
We have been given an equation.
x/2 + x/3 =15
We need to find the solution of given equation.
First we simplify the LHS of given equation.
x/2 + x/3
= (3x + 2x) / (2)(3)
= 5x / 6
So given equation would be,
⇒ x/2 + x/3 = 15
⇒ 5x / 6 = 15
⇒ 5x = (15)(6)
⇒ 5x = 90
⇒ x = 18
We need to check above solution.
Substitute x = 18 in LHS of given equation.
= 18/2 + 18/3
= 9 + 6
= 15
= RHS
Therefore, the solution of the given equation x/2 + x/3 = 15 is x = 18
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The area of a rectangle is 85 yd 2 . If both the length and the width of the rectangle are doubled, what is the area of the new (bigger) rectangle?
The area of the rectangle if both the length and the width of the rectangle are doubled is 340 yd²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the length and y represent the width of the rectangle. The area is 85 yd², hence:
xy = 85
If both the length and the width of the rectangle are doubled:
new length = 2x; new width = 2y
new area = 2x * 2y = 4xy = 4(85) = 340 yd²
The area of the rectangle if both the length and the width of the rectangle are doubled is 340 yd²
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Each of these sequence or series formulas involves four quantities that are represented by a variable. For each fomula, describe the four quantities.
c. a n = a₁ rⁿ⁻¹
The four Quantities are a1 , r, n , [tex]S_{n}[/tex]
What is a Series:
A series can be highly generalized as the sum of all the terms in a sequence. However, there has to be a definite relationship between all the terms of the sequence.
Arithmetic progression
an = a1 + ( n-1) d
a1 is the first term
d =common difference
an is the nth term
an can be found out if we know the a1 , d and n
b) Arithmetic progression
a1 is the first term
an is the nth term
sn is the sum of the n terms of the series
Sn = n/2 ( a1 + an)
we can calculate sn if we know a1 , an and n
c)Geometric progression
an = a1rn-1
a1 is the first term
an is the nth term
r is the common ratio
we can calculate an if we know a1 , r and n
d)Geometric progression
Sn = a1( 1- rn) / 1 - r
a1 is the first term
r is the common ratio
sn is the sum of the n terms of the series
If we know a1 , r and n we can calculate [tex]S_{n}[/tex].
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osslyn is thinking of a number, n and she wants her sister to guess the number. Her first clue is that eight less than two times her number is between two and six (inclusive). Write a compound inequality that shows the range of numbers that Josslyn might be thinking of.
The required number that is guessed is 2x - 8 where inequality 2 < x < 6.
Given that,
Osslyn is thinking of a number, n.
Her first clue is that eight less than two times her number is between two and six (inclusive).
To write a compound inequality that shows the range of numbers that Josslyn might be thinking of.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the number be x,
According to the question,
Gusset number = 2x - 8, where x is between 2 and 8 implies
2 < x < 6
Thus, the required number that is guessed is 2x - 8 where inequality 2 < x < 6.
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help me understand the linear equation
Answer:
y = 4x - 4
Step-by-step explanation:
Slope intercept follows the form y = mx + b
m represents the slope
b represents the y intercept
To find the slope of a table you can find the constant change in y over the constant change in x. The y values 0, 4, 8, 12 are increasing by 4 every point meaning the change in y is 4. The x values 1, 2, 3, 4 are increasing by 1 every point meaning the change in x is 1. Making the slope 4/1 or just 4.
Now use what you know: y = 4x + b to find b, we can use any of the coordinate points to substitute. I'm going to use point (1,0) where 1 is the x value and 0 is the y value.
y = 4x + b
0 = 4(1) + b
Solve for b
b = -4
:)
Simplify by combining like terms. 0.5 g+g
The simplification by combining like terms of 0.5g + g is 1.5g.
According to the given question.
We have an expression 0.5g + g .
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression 0.5g + g.
Here 0.5g, and g both are the like terms.
So, we add coeffcients of g to simplify the given expression.
Therefore, the simplification of 0.5g + g is given by
0.5g + g
= 1.5g
Hence, the simplification by combining like terms of 0.5g + g is 1.5g.
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Determine the slope of the line that contains the given points.
T(-6,-11), V(-12,-10)
The slope of the line containing (-6,-11) and (-12,-10) is (-1/6).
The slope of a straight line can be written as follows,
m = [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex] equation1
The line is containing the points (-3,3) and (4,3). So, we can write
[tex]y_{2}[/tex] = -10 , [tex]y_{1}[/tex] = -11 , [tex]x_{2}[/tex] = -12 , and [tex]x_{1}[/tex] = -6 .
On substituting the values of variables in equation1, we will get
m = ( (-10)-(-11) ) / ( (-12)-(-6) ) = (1/(-6)) = (-1/6).
As the slope of a line is (-1/6), so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (-6,-11) and (-12,-10) is (-1/6).
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< Exit
1-4: MathXL for School: Additional Practice
Assignment is past due (09/13/22 11:59pm)
A 150-pound person uses 5.6 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 180 calories?
CH
Answer:
32,14 minutes
Step-by-step explanation:
5.6 calories per hour = 5.6 x 60 = 336 calories per hour
So in 1 hour, that person will lose 336 calories
To lose only 180 calories time he should walk = 180/336 hour = 180/336 x 60 = 32,14 minutes
We can figure out our answer is in the ballpark by noting that 336/2 = 168
So to lose 168 calories, the person should walk for 1/2 hour so since 180 is slightly greater than 168, the person should walk for slightly more than half-hour
Forty two is the sun of twelve and the product of a number and 3. What is the number. (Show work)
Answer:
10
Step-by-step explanation:
First write out the equation: 42 = 12 + 3x
42 - 12 = 12 - 12 + 3x
30 = 3x
30/3 = 3x/3
x = 10
HELP How do i calculate the surface area
Answer:
384, 576
Step-by-step explanation:
The surface area is
[tex]2(12 \cdot 6+12 \cdot 6+6\cdot 8)=384[/tex]
The volume is
[tex](12)(8)(6)=576[/tex]
Position and label each triangle on the coordinate plane. (Lesson 4-8)
Right ΔXYZ with hypotenuse XZ, Z Y is twice X Y , and XY is b units long.
Insert the triangle into the first quadrant. Z's y-coordinate is 0 because it is on the x-axis. Because the leg is 3b units long, its x-coordinate is 3b. Y's X-coordinate is 0 because it is on the y-axis. Because the leg is b units long, its y-coordinate is b.
What is a triangle with coordinates?
The term triangular coordinates can refer to at least three related systems of coordinates in the Euclidean plane: a special case of barycentric coordinates for a triangle, also known as a ternary plot or areal coordinates, among other things.
Because this is a right triangle, two of its sides can be found on the axes. Placing the triangle's right angle at the origin will allow the two legs to be parallel to the x- and y-axis.
Insert the triangle into the first quadrant. Z's y-coordinate is 0 because it is on the x-axis. Because the leg is 3b units long, its x-coordinate is 3b. Y's X-coordinate is 0 because it is on the y-axis. Because the leg is b units long, its y-coordinate is b.
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Describe the Domain
f(x)=-3x²+2
Answer:
X€R or x€(-&, +&)......
