This gives us the answer of 1.9 miles, meaning that he must ride an average of 1.9 miles each day for the remaining 4 days of the week in order to reach his goal of 39.6 miles.
(39.6 - 8) ÷ 4 = x
7.6 ÷ 4 = x
x = 1.9 miles
Bentley wants to ride his bicycle 39.6 miles this week. He has already ridden 8 miles, leaving him with 31.6 miles left to ride. He has 4 days left to ride, so we need to figure out how many miles he must ride each day in order to meet his goal. We can do this by subtracting the 8 miles he has already ridden from the total goal of 39.6 miles. This gives us 31.6 miles remaining to be ridden. We then divide this number by 4, since he has 4 days left in the week to ride. This gives us the answer of 1.9 miles, meaning that he must ride an average of 1.9 miles each day for the remaining 4 days of the week in order to reach his goal of 39.6 miles.
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Find the distance between the two points in simplest radical form.
(-4, -6) and (2, -1)
The distance between the two points is [tex]\sqrt{61}[/tex]
Explanation:
Given that the two points are [tex](-4,-6)[/tex] and [tex](2,-1)[/tex]
We need to determine the distance between the two points in simplest radical form.
The distance between the two points can be determined using the
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let us substitute the coordinates [tex](-4,-6)[/tex] and [tex](2,-1)[/tex] in the above formula, we get,
[tex]d=\sqrt{(2+4)^2+(6+1)^2}[/tex]
Simplifying the terms, we get,
[tex]d=\sqrt{(6)^2+(7)^2}[/tex]
Squaring the terms, we get,
[tex]d=\sqrt{36+49}[/tex]
Adding, we get,
[tex]d=\sqrt{85}[/tex]
Simplifying, we have,
[tex]\sqrt{61}[/tex]
Thus, the distance between the two points in simplest radical form is [tex]\sqrt{61}[/tex]
John claims that more than 25% of Wenatchee population prefer TACO BELL. To support his claim, he selected a sample of 200 people in Wenatchee and observed that 63 prefer Taco Bell. At a= 0.05, is
there enough evidence to support his claim? Justify your answer by stating what is (a) the null hypothesis and alternative hypothesis. Explain what test (left-tailed, right-tailed or two-tailed) you are using. Also find
(b) critical z-value (not the p-value!)
(c) test value
Hint: You can use the formula for z-Test for proportion
The test value is 0.636, and the critical z-value is 1.645. Since the test value (0.636) is greater than the critical z-value (1.645), we reject the null hypothesis and conclude that there is enough evidence.
What is test value?It is usually represented by the number of errors or defects found in a system or component during a test phase.
For this test, we use the formula for a z-test for proportions.
Let p be the proportion of Wenatchee population that prefers Taco Bell.
Null hypothesis: p = 0.25
Alternative hypothesis: p > 0.25
The critical z-value for this test is 1.645, which is the z-value corresponding to a=0.05.
The test value is calculated by taking the sample proportion of people preferring Taco Bell
(63/200 = 0.315)
and subtracting the null hypothesis proportion of people preferring Taco Bell (0.25).This gives us 0.065.
This value is then divided by the standard error of the proportion, which is calculated as the square root of
(p*(1-p)/n), where p is the null hypothesis proportion (0.25) and n is the sample size (200). This gives us a value of 0.636.
Therefore, the test value is 0.636, and the critical z-value is 1.645.
Since the test value (0.636) is greater than the critical z-value (1.645), we reject the null hypothesis and conclude that there is enough evidence to support John's claim that more than 25% of Wenatchee population prefer TACO BELL.
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The mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is .35. If the price increases by 25 cents a box, what is the new variance?
The new variance is 0.0625 / n
We can use the following formula to calculate the variance of a data set
variance = (sum of (x - mean)^2) / (number of data points)
where x is a data point and mean is the mean of the data set.
If the mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is 0.35, we can find the standard deviation as follows
standard deviation = square root of variance = sqrt(0.35) = 0.59
Now, if the price increases by 25 cents a box, the new mean cost will be
new mean = $4.00 + $0.25 = $4.25
To find the new variance, we need to calculate the sum of (x - mean)^2 for the new data set and divide by the number of data points. Let's assume we are still considering the same number of boxes.
sum of (x - mean)^2 = [(4.25 - 4)^2 × n] = 0.0625 × n
where n is the number of data points.
Therefore, the new variance can be calculated as
new variance = (sum of (x - mean)^2) / (number of data points) = 0.0625 / n
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A bottle of juice costs 9.40. If the price of the juice increased by 15%, what is
the new price of the juice after the increase?
Answer:
price of the juice increased by 15%, then the new price of the juice is: New price = Old price + (Percent increase * Old price) Percent increase = 15% Old price = $9.40 New price = $9.40 + (0.15 * $9.40) New price = $9.40 + $1.41 New price = $10.81 Therefore, the new price of the juice after the increase is $10.81.
PLEASE HELP NEOWWWW
Select the best interpretation of the following inequality. ∣−2.2−x∣>3
A) The distance between -2.2 and -x is greater than 3.
B) The distance between -2.2 and x is greater than 3.
C) The distance between 3 and -2.2 is greater than x.
Answer:
B) The distance between -2.2 and x is greater than 3.
Step-by-step explanation:
in the rhombus below, m<1 = 9x, m<2 = x + y, m<3 =18z find the value of each variable. x = _________ y = _______ z = ______
The value of each variable include the following:
x = 10.
y = 80.
z = 5.
What is a rhombus?In Mathematics and Geometry, a rhombus refers to a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal).
Additionally, a rhombus typically has two (2) diagonals that bisect each other at right angles (90 degrees). This ultimately implies that, all of the three angles are 90 degrees;
m∠1 = 9x = 90
9x = 90
x = 90/9
x = 10
m∠2 = y + x = 90
y + x = 90
y + 10 = 90
y = 90 - 10
y = 80
m∠3 = 18z = 90
18z = 90
z = 90/18
z = 5
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Is the function is even, odd, or neither? How do you know?
The function given in graph is an odd function.
What is the definition of a function?
In mathematics, a function is a rule that assigns a unique output to each input in a given set. In other words, a function is a relationship between two sets, called the domain (set of possible inputs) and the range (set of possible outputs), such that each input is paired with exactly one output.
Now,
In mathematics, an even function is a function f(x) that satisfies the following property: f(-x) = f(x) for all values of x in the domain of the function. The graph of an even function is symmetric about the y-axis, meaning that if you fold the graph along the y-axis, the two halves will be identical.
On the other hand, an odd function is a function f(x) that satisfies the following property: f(-x) = -f(x) for all values of x in the domain of the function. In other words, an odd function is symmetric with respect to the origin. The graph of an odd function is symmetric about the origin, meaning that if you rotate the graph 180 degrees about the origin, the graph will look the same.
As we can see the graph will be same when we will rotate it 180°.
Hence,
Given function is odd function.
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if the given triangles are similar find the missing length
Answer 24 do you enderstand?
Leila buys candy that costs $7 per pound. She will spend less than $42 on candy. What are the possible numbers of pounds she will buy?
Use p for the number of pounds Leila will buy.
Write your answer as an inequality solved for p.
Answer:
If you spent $56 on candy, she'd buy 8 pounds.
Step-by-step explanation:
hi!!
pls answer this
worth 93 points!!!
screenshot and circle plsss
Answer:
a. already done
b. x=3, x=4, and x=5
c. x=2, x=3, x=4, and x=6
Step-by-step explanation:
The < symbol means less than, so all values of x less than what is stated are correct
The ≤ symbol means less than or equal to, so all values of x less than, and what is stated are correct
The answer is in the screenshot.
Let me know if it helps
a 95 confidence interval for p1-p2 is (-0.185, -0.093). explain how the confidence interval provides the same information as the significance test in part a
We can conclude that the difference between p1 and p2 is statistically significant at the 5% level of significance.
The confidence interval and significance test in part A both provide similar information. The significance test in part A tests if the difference between p1 and p2 is statistically significant, while the confidence interval provides an estimated range of values for the true difference between p1 and p2 with a certain degree of confidence (95% in this case).A confidence interval is a range of values that we believe will include a population parameter with a specified level of confidence.
It can be computed to estimate the population mean or the difference between two population means, such as p1 and p2.In contrast, a significance test assesses whether the difference between two population proportions is statistically significant.
The test calculates a p-value, which is the likelihood of obtaining the observed difference between two proportions, assuming the null hypothesis (that there is no difference between the two proportions) is true. A p-value less than the level of significance (usually 0.05) indicates that the difference between the two proportions is statistically significant, while a p-value greater than the level of significance indicates that the difference is not statistically significant.
Both the confidence interval and the significance test inform us about the difference between two population proportions. The confidence interval provides a range of plausible values for the difference, while the significance test tells us whether the difference is statistically significant or not. In this particular case, since the confidence interval does not contain zero,
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Pronghorn Co. Has equipment that cost $78,200 and that has been depreciated $49,900. Record the disposal under the following assumptions. It was sold for $19,500. It was sold for $30,800
the disposal under the following assumptions are: To Equipment $78,200
Being equipment is scrapped at a gain
a)
Particulars Debit Credit
Loss on disposal $28,300
Accumulate depreciation of $49,900
To Equipment $78,200
Being equipment scrapped with no value
b)
Particulars Debit Credit
Loss on disposal $8,800
Accumulate depreciation of $49,900
Cash $19,500
To Equipment $78,200
Being equipment disposed of at a loss
c)
Particulars Debit Credit
Accumulate depreciation of $49,900
Cash $30,800
To Gain on disposal $2,500
To Equipment $78,200
Being equipment is scrapped at a gain
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PLLS help me with this two. answer like (A).... (B)..... (C)...
(a) The transformation that maps ΔSTU to ΔLMN is a translation of three units to the right and one unit up, followed by a counterclockwise rotation of 90° around the origin
What is transformation?
A dilation with respect to the origin by a scale factor of 1/3.
To map ΔSTU to ΔLMN, we need to perform a combination of transformations: a translation, a rotation, and a dilation.
First, we translate triangle STU three units to the right and one unit up to get triangle S'T'U', where S'(1,3), T'(-2,5), and U'(0,-2).
Next, we rotate triangle S'T'U' 90 degrees counterclockwise around the origin to get triangle S''T''U'', where S''(3,1), T''(-5,2), and U''(2,0).
Finally, we dilate ΔS''T''U'' by a scale factor of 1/3 with respect to the origin to get ΔLMN, where L(1/3,1/3), M(-5/3,2/3), and N(2/3,0).
Therefore, the transformation that maps ΔSTU to ΔLMN is a translation of three units to the right and one unit up, followed by a counterclockwise rotation of 90° around the origin, and finally a dilation with respect to the origin by a scale factor of 1/3.
(b) The side overline SU corresponds to the side overline LN.
(c) Yes, corresponding sides are congruent. the triangles are congruent by the Side-Side-Side (SSS) congruence criterion.
What is congruent?
We can see this by calculating the length of each side of the two triangles:
Length of ST = distance between points S and T = √(((-5) - (-2))² + ((4) - (2))²) = √(10)
Length of LM = distance between points L and M = √(((-5/3) - (1/3))² + ((2/3) - (1/3))²) = √(10)/3
Length of TU = distance between points T and U = √(((-5) - (-3))² + ((4) - (-3))²) = √(74)
Length of MN = distance between points M and N = √(((-5/3) - (2/3))² + ((2/3) - 0)²) = √(10)/3
Length of US = distance between points U and S = √(((-3) - (-2))² + ((-3) - (2))²) = √(26)
Length of NL = distance between points N and L = √(((2/3) - (1/3))² + ((0) - (1/3))²) = √(2)/3
All corresponding sides have the same length, so the triangles are congruent by the Side-Side-Side (SSS) congruence criterion.
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True or False: Simple random sample gets us independence, and the success-failure conditions is satisfied since 289 and 400−289 = 111 are both at least 10
the statement is true.the success-failure condition is satisfied and we can conclude that simple random sample gets us independence.
Simple random sampling is a type of probability sampling technique wherein every member of the population has an equal and independent chance of being selected. Independence means that the selection of one unit does not affect the selection of any other unit. The success-failure condition is an important condition of simple random sampling, which states that the size of each of the two groups (i.e., success and failure) should be at least 10. In this case, the two groups are 289 and 111, which are both greater than 10. Therefore, the success-failure condition is satisfied and we can conclude that simple random sample gets us independence.
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HEEELLLPPP I WILL GIVE YOU A BRAINILIST, find the Regression Equation and the final answer
Equation for the regression line is given as y = -0.95X + 8.99.
When the wind is blowing at a speed of 27 mph, the chill factor is -16.66.
What does a regression line mean?Regression coefficients are estimates of specific unknown properties that explain the relationship between a predictor variable and the related response.
In order to extrapolate the value of an unknown variable from a known variable, regression coefficients are used. The effect of a one-unit change in an independent variable on the dependent variable can be measured via linear regression by determining the equation of the best-fitted straight line. The procedure in question is regression analysis.
Calculation Overview
X's total is 45.
Total Y = 20
Mean X = 6.4286
Mean Y = 2.8571
Square sum (SSX) equals 113.7143.
Product total (SP) = -108.5714
Regression Equation = ŷ = bX + a
b = SP/SSX = -108.57/113.71 = -0.95477
a = MY - bMX = 2.86 - (-0.95*6.43) = 8.99497
y = -0.95477X + 8.99497
y = -0.95X + 8.99
The wind speed chill factor when it is 27 mph.
Using the output of the regression line shown above, we would solve for this.
y=-0.95X+8.99
y=-0.95X+8.99
y = -0.95 * 27 + 8.99
y = -25.65 + 8.99
y = -0.95 * 27 + 8.99
Conclusion: y = -16.66
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Some students in Grade 7 and Grade 8 take a survey about whether they would prefer to join
a movie club or a music club. The table shows the results. The students want to make a two-
way relative frequency table using row totals.
Complete each row. Round to the nearest
hundredth. You can use a calculator to help.
Movie Club Music Club Total
1.00
0.61
Grade 7
Grade 8 0.25
Total
0.39
?
1.00
Grade 7
Grade 8
Total
Movie Club Music Club
20
13
12
15
32
28
Total
33
27
60
The frequency distribution table for the question is :
Grade 7 | 0.67 | 0.33 | 1.00
Grade 8 | 0.42 | 0.58 | 1.00
Total | 1.09 | 0.91 | 2.00.
What is frequency?Frequencies refer to the number of times an event or a value occurs in a dataset. It is a count of the occurrences of a particular value or event. Frequencies are commonly used in statistics to summarize data and to help understand patterns in a dataset. The frequency of a value can be expressed as an absolute frequency (the number of times a value occurs) or a relative frequency.
The given table shows the results of a survey conducted among students in Grade 7 and Grade 8 about their preference for joining a movie club or a music club. The students want to make a two-way relative frequency table using row totals. In the table, the row totals represent the total number of students in each grade, and the column totals represent the total number of students who want to join each club.
To complete the table, we need to find the missing values. For example, in the row for Grade 7, the total number of students is 33. We know that 20 of these students want to join the movie club, so the relative frequency of Grade 7 students who want to join the movie club is 20/33, which is approximately 0.61. Similarly, we know that 13 Grade 7 students want to join the music club, so the relative frequency of Grade 7 students who want to join the music club is 13/33, which is approximately 0.39.
Likewise, we can find the missing values in the other rows and complete the table. The completed table shows the relative frequency of students in each grade who want to join each club. For example, 0.61 or approximately 61% of Grade 7 students want to join the movie club, while 0.25 or approximately 25% of Grade 8 students want to join the movie club.
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Which equation is inverse to the equation
The expression which represents this condition is x=-15z/y
Define Inverse variation meansA link between two variables known as inverse variation occurs when one variable's value rises while the other one's value falls, and vice versa. Inverse variation can be represented mathematically as y = k/x, where y and x are the variables, k is the constant of proportionality, and the product of y and x is constant.
When the value of x increases the value of y decreases.
When the value of x decreases the value of y increases.
So for an inverse variation we have the expression
y=k/x or
x=k/y
The expression which represents this condition is
x=-15z/y
Hence option b) or the second option is the right answer.
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The complete question is attached below.
write an expression that is equivelent to 1/4x +1 3/4x- 2/3-1/2x
The expression equivalent is 9+2x/6x
What is a fraction?A fraction is a part of a whole. It is the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator
1/4x +1 3/4x - 2/3-1/2x
1/4x + (4x + 3/4x) - 2/3 - 1/2x
(1 + 4x + 3)/4x - (4x - 3)/6x
4 + 4x/4x - 4x - 3/6x
(3(4 + 4x) - 2(4x - 3))/12x
(12 + 12x - 8x + 6)/12x
(18 + 4x)/12x
(9 + 2x)/6x
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Y is directly proportional to x
When y=30 x=6
work out an equation connecting y and x
The relation between x and y is defined by the equation: y = 5x, where % is constant of the equation and X and Y are variable.
It is given that y varies directly as x. It means y is proportional to x.
y ∝ x
y = kx
{Where k is constant of proportionality.}
It is given that y=30 when x=6. Put x=5 and y=25 in the above equation to find the value of k.
30 = k(6)
Divide both sides by 6.
The value of k is 5.
Hence The relation between x and y is defined by the equation: y = 5x.
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i need the answer to all questions
Answer:
here's your answerhope it will help you ( ꈍᴗꈍ)(✿^‿^)(✿^‿^)!!!
Unit 2: Logic & Proof
Homework 2: Compound Statements
A combination of two or more simple statements is a compound statement. The connectives generally used in mathematics are ‘and’, ‘or’, ‘if ’, ‘if and only if’.
In mathematics, like in any language, compound statements are created by combining simpler ones using connectives. The truth value of a compound statement is determined by the truth value of its smaller components.
There are four compound statements:
1. ¬p , Not p (i.e. the negation of p) : Negation
2. p ∧ q, p and q : Conjunction
3. p ∨ q, p or q : Disjunction
4. p → q, If p then q : Conditional
Beginning with the premise that P (the hypothesis) is true, we create a chain of implications, each of which has previously been proven to be true, ultimately leading to Q. (the conclusion). Imagine the chain has six consequences. As a result, the direct proof technique may be expressed combination as follows:
P, P ⇒ P1, P1 ⇒ P2, P2 ⇒ P3, P3 ⇒ Q1, Q1 ⇒ Q2, Q2 ⇒ Q.
If P and the implications in the previous chain are all true, we must derive that Q is likewise true logically. But, according to the truth table for P ⇒ Q, knowing that P ⇒ Q is a true statement does not indicate that P or Q are true, just that the inference is true. Recall that P can be false, Q can be true or false, and the inference might be true or false.
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Question: What are Compound Statements? Write proof and logic for the statements.
what is the value of x :?
2x = 3x - 45
[tex] \: \: \\ [/tex]
[tex] \\ [/tex]
Thanks:)
Answer:
2x-3x=-45
-x=-45
x=45
by simple method
a table shows information about the masses of some dogs what is the minimum number of dogs that could have a mass of 26kg
6 dogs are the bare minimum that might weigh more than 24 kg.
What do minimum and maximum value mean?
Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.
For example, if we have a set of numbers {2, 4, 6, 8, 10}, the minimum value is 2 because it is the smallest number in the set, while the maximum value is 10 because it is the largest number in the set.
The minimum of the values present in the interval 20 to 40 is 6
The maximum of the values present in the interval 20 to 40 is (12+6) = 18
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Find an equation of a circle centred
Center - radius equation for circle of radius r ,centered at (h,k) is :
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]
you have r = √21
[tex]r^{2} =[/tex] (√21)^2 = 21
centre (h,k) = (0,0) so h =0 and k =0
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]
[tex](x-0)^{2} + (y -0)^2 = 21[/tex]
[tex]x^{2} + y^{2} = 21[/tex]
How does the volume of a cone relate to the volume of a cylinder with
a congruent base and the same height?
1 The volume of the two figures are the same
2 The volume of the cone is 3 times as large
3 The volume of a cylinder is twice as large
4 The volume of the cone is 1/3 as large
The comparison of the volume of a cone relative to the volume of a cylinder with the same dimensions is given as follows:
4 The volume of the cone is 1/3 as large.
How to obtain the volume a cone?The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.
V = πr²h/3.
For the volume of the cylinder, the equation is given as follows:
V = πr²h.
The volume of the cylinder is triple the volume of the cone, hence the volume of the cone is one third of the volume of the cylinder.
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A carnival charges a $10 entrance fee and $2 per ride. Write an equation to represent this situation.
y = mx + b
Answer:
y = 2x + 10
Step-by-step explanation:
What we know:
10 dollar entrance fee
2 dollars PER ride
"per" is an important word since it tells us that the x will be there.
That means that, if its a 10 dollar entrance fee and 2 dollars per ride, it will be 2x + 10.
[tex]y=2x+10[/tex]
what number is 120% more than 180?
how do you solve this step by step
txs for the help
Will mark Brainliest
Solve the exponential equation for x:
7^3-5x=(1/49)^2x+9
Answer:
x = 21
Step-by-step explanation:
Given exponential equation:
[tex]7^{3-5x}=\left(\dfrac{1}{49}\right)^{2x+9}[/tex]
Rewrite 49 as 7²:
[tex]7^{3-5x}=\left(\dfrac{1}{7^2}\right)^{2x+9}[/tex]
[tex]\textsf{Apply the exponent rule:} \quad \dfrac{1}{a^n}=a^{-n}[/tex]
[tex]7^{3-5x}=\left(7^{-2}\right)^{2x+9}[/tex]
[tex]\textsf{Apply the exponent rule:} \quad (a^b)^c=a^{bc}[/tex]
[tex]7^{3-5x}=7^{-2(2x+9)}[/tex]
Simplify the exponent:
[tex]7^{3-5x}=7^{-4x-18}[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]
[tex]3-5x=-4x-18[/tex]
Add 4x to both sides:
[tex]3-5x+4x=-4x-18+4x[/tex]
[tex]3-x=-18[/tex]
Subtract 3 from both sides:
[tex]3-x-3=-18-3[/tex]
[tex]-x=-21[/tex]
Divide both sides by -1:
[tex]x=21[/tex]
Therefore, the value of x is 21.
Answer:
Will mark Brainliest
Solve the exponential equation for x:
7^3-5x=(1/49)^2x+9
Express in simplest radical form
Jules owns a square plot of land that measures 30 yards on each side. He plans to divide the land in half by building a fence, as shown by the dotted line below. How many yards of fencing will Jules need?
15 yd
30 yd
30 StartRoot 3 EndRoot yd
30 StartRoot 3 EndRoot yd
Using the Pythagorean theorem, we get,
Jules will need the fencing length of 30√2 yards to build the square fence. Hence, option (c) is correct.
It can be defined as a rectangle whose two adjacent sides are equal. Single regular polygon with equal interior angles, central and exterior angles (90°), and equal diagonal lengths
Given data:
The length of each side of the yard is AB = BC = CD = AD = 30 yards.
As shown by the dotted line, the fencing should be done along the diagonal BD of the given square plot. Then, applying Pythagoras' theorem to find the fencing length BD as,
BD² = BC²+ CD²
Substitute the values as
BD² = 30² + 30²
⇒ BD² = 900+ 900
⇒ BD² = 1800
⇒ BD = √1800
⇒ BD = 30√2 yards.
Thus, we can conclude that Jules will need the fencing length to build the fence along the square plot. Therefore, option (c) is correct.
Learn more about Pythagorean theorem:
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