The coordinates of point r(-8,0).
What is midpoint formula in coordinate geometry?The coordinates of the point r(x,y) which divides the line segment joining the points p([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and q([tex]x_{2}[/tex],[tex]y_{2}[/tex]) internally in the ratio :[tex]m_{1}[/tex][tex]m_{2}[/tex] are
[tex]\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)[/tex]
Given that,
Two end points on the line q(-14,0) and s(2,0). point r(x,y) is the partition of the line segment from q to s in a ratio 3:5
[tex]m_{1}[/tex] = 3 and [tex]m_{2}[/tex] = 5
By using the midpoint formula
[tex]\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)[/tex]
[tex]\left(\frac{3(2)+ 5(-14) }{3+5 } ,\frac{3(0)+ 5(0) }{3+5 }\Rifgt)[/tex]
[tex]\left(\frac{-64}{8 } ,\frac{0 }{8 }\Rifgt)[/tex]
[tex]\left(-8 ,0\Rifgt)[/tex]
Hence, The coordinates of point r(-8,0).
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Find the Perimeter of the figure below, composed of a parallelogram and one
semicircle. Rounded to the nearest tenths place
4
14
The perimeter of the figure to the nearest tenth is 44.6 units
Perimeter of a figure?The perimeter of a figure is the sum of the whole sides.
Therefore,
A parallelogram has opposite sides equal to each other.
Therefore, the perimeter of the figure is as follows;
The figure combines a parallelogram and a semi circle.
Therefore,
perimeter of the figure = 4 + 14 + 14 + πr
perimeter of the figure = 32 + 3.14 × 4
perimeter of the figure = 32 + 12.56
perimeter of the figure = 44.56
perimeter of the figure ≈ 44.6 units
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Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range:
For the given data set
Minimum = 48
Lower quartile = 55
Median = 63.5
Upper quartile = 74
Maximum = 80
Interquartile range = 19
Measures of a DataFrom the question, we are to determine the minimum, lower quartile, median, upper quartile, maximum, and interquartile range of the given data set
The given data set is
48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80
Minimum = 48
Lower quartile = (54+56)/2
Lower quartile = 110/2
Lower quartile = 55
Median = (63+64)/2
Median = 127/2
Median = 63.5
Upper quartile = (74+74)/2
Upper quartile = 148/2
Upper quartile = 74
Maximum = 80
Interquartile range = Upper quartile - Lower quartile
Interquartile range = 74 - 55
Interquartile range = 19
Hence, for the given data set
Minimum = 48
Lower quartile = 55
Median = 63.5
Upper quartile = 74
Maximum = 80
Interquartile range = 19
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Find the measure of x.
16
X
38°
x = [?]
Round to the nearest hundredth.
The answer is.........
25.99
[tex]2x+5\ \textless \ \frac{x+1}{4}[/tex]
Answer:
x < -19/7
Step-by-step explanation:
Solve for x
2x+5 < (x+1)/4
Multiply each side by 4
4( 2x+5) < (x+1)/4 *4
8x + 20 < x+1
Subtract x from each side
8x+20-x < x+1-x
7x + 20 < 1
Subtract 20 from each side
7x+20-20 < 1-20
7x< -19
Divide by 7
7x/7 < -19/7
x < -19/7
Answer:
[tex] \red{x < \frac{ - 19}{7} }[/tex]
Step-by-step explanation:
[tex]2x + 5 < \frac{x + 1}{4} \\ \text{use \: cross \: muliplication} \\ 4(2x + 5) < x + 1 \\ 8x + 20 < x + 1 \\ 8x - x < - 20 + 1 \\ 7x < - 19 \\ \frac{7x}{7} < \frac{ - 19}{7} \\ x < \frac{ - 19}{7} [/tex]
Mr. jimenez deposited money into an account in which interest is compounded quarterly at a rate of 2.6%. how much did he deposit if the total amount in his account after 4 years was $7160.06, and he made no other deposits or withdrawals? $6455 $6455 $6798 $6798 $6887 $6887 $6977 $6977 skip to navigation
Answer:
$6455.
Step-by-step explanation:
The formula for this investment is:
A = P(1 + r/4)^4t where P = amount deposited , A amount after t years,
r = rate (as a decimal fraction).
So we have:
7160.06 = P(1 + 0.026/4)^16
7160.06 = P * 1.109227
P = 7160.06 / 1.109227
= $6455.
Find the volume of the cylinder.
Either enter an exact answer in terms of pi or use 3.14 for pi
4
6
Answer:
144π or 452.16 units³
Step-by-step explanation:
The formula for volume of a cylinder is [tex]\pi r^2 h[/tex]. We can use the given values for radius and height to find the volume of the cylinder.
Finding the Volume[tex]V=\pi r^2 h\\V=\pi6^2(4)\\V=\pi36(4)\\V=144\pi \ OR\ 452.16[/tex]
The volume of the cylinder is 144π or 452.16 units³.
Sloane kicked a soccer ball off the ground at a speed of 36 feet per second. the height of the ball can be represented by the function h(t) = −16t2 36t where t is the time in seconds. . how many seconds did the ball travel before returning the ground? t = 0.44 seconds t = 2.25 seconds t = 16 seconds t = 36 seconds
The total time in seconds the ball will take to travel before returning the ground is 2.25 seconds.
What is factorisation?The breaking or breakdown of an entity (such as an integer, a matrices, or a polynomials) into a products of another unit, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring in mathematics.
Calculation for the time;
Let 't' be the time in second the ball will travel.
Let H(t) be the total height travelled by the ball.
The equation of the height is given as
[tex]H(t)=-16 t^{2}+36 t[/tex]
As soon as the ball will return to the ground the total height will become zero.
So, put equation of height equal to zero.
[tex]-16 t^{2}+36 t=0[/tex]
Factorise the above equation;
[tex]-16 t\left(t-\frac{9}{4}\right)=0[/tex]
Put each value equals to zero to get the value of time.
[tex]\begin{aligned}&t=0 \mathrm{sec} \\&t=9 / 4=2.25 \mathrm{sec}\end{aligned}[/tex]
As, time can not be zero
Therefore, the total time taken by the ball to return to the ground is 2.25 sec.
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Identify the ellipses, represented by equations, whose eccentricities are less than 0.5.
Ellipses that are represented by equations, whose eccentricities are less than 0.5 are:
(A) 49x2 -98x + 64yz +256y -2,831 = 0 (B) 81x2 -648x +100yz +200y -6,704 = 0 (F) 64x2 +512x +81y2 -324y -3,836 = 0What is an equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.To identify the ellipses:
For the standard-form equation of an ellipse: Ax^2+Bx+Cy^2+Dy+E=0
We can define:
p=min(A,C)q=max(A,C)Then the eccentricity can be shown to be:
e=(1-p/q)p/q=1-e^2For Eccentricity<0.5, we want:
p/q>3/4Checking the values of p/q for the given equations, we have p/q= equations (A), (B), and (F) are of ellipses with eccentricity < 0.5.
Therefore, ellipses that are represented by equations, whose eccentricities are less than 0.5 are:
(A) 49x2 -98x + 64yz +256y -2,831 = 0 (B) 81x2 -648x +100yz +200y -6,704 = 0 (F) 64x2 +512x +81y2 -324y -3,836 = 0Know more about equations here:
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The complete question is given below:
Identify the ellipses, represented by equations, whose eccentricities are less than 0.5.
(A) 49x2 -98x + 64yz +256y -2,831=0
(B) 81x2 -648x +100yz +200y -6,704 =0
(C) 6x2 -12x +54y2 +108y -426 =0
(D) 49x2 + 196x +36y2 +216y -1,244 =0
(E) 4x +32x +25y2 - 250y +589 =0
(F) 64x2 +512x +81y2 -324y -3,836 =0
Enter the correct answer in the box.
This graph represents a transformation of the parent square root function.
-10-8 -6
A
-2
10-
8
6-
2-
-2-
-4-
-6-
-8-
-10-
O
2
6 8 10
➜X
Replace the values of h and k to create the equation of the transformed function.
Answer:
Step-by-step explanation:
The most basic quadratic function is f(x) = x2, whose graph appears below. ... us to graph an entire family of quadratic functions using transformations.
Which is the approximate solution to the system y = 0.5x + 3.5 and y = −A system of equations. y equals 0.5 x plus 3.5. y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction.x + shown on the graph?
The approximate solution to the given system of equation is (-2.71, 2.14)
Solving a system of linear equationsFrom the question, we are to determine the approximate solution to the given system of linear equations.
The given equations are
y = 0.5x + 3.5
y = -2/3 x+ 1/3
From the given information, we are to show the solutions on a graph
The graph that shows the solution to the given system of equation is shown below.
The solution to the given system is the point of intersection of the lines. The coordinate of the point of intersection of the lines is (-2.71, 2.14). That is, x = -2.71, y = 2.14.
Hence, the approximate solution to the given system of equation is (-2.71, 2.14)
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A ladder resting against a wall makes an
angle of 63° with the ground. The foot of
the ladder is 4.7 m from the wall.
Calculate the height of the top of the
ladder above the ground
Answer:
9.224
Step-by-step explanation:
Answers are needed urgently..ty
Angle <QAB is =15° because the opposite angles of an isosceles triangle are equal.
The length of the straight line AB = 80cm
Calculation of angle of a triangleThe angle at a point = 360°
Angle AQB= 360 - 210° = 150
But the angle that makes up a triangle= 180°
180-150= 30°
But <QAB = <QBA because triangle AQB is an isosceles triangle.
30/2 = 15°
To calculate the length of the straight line the following is carried out using the sine laws.
a/ sina, = b sinb
a= 8cm, sin a { sin 15)
b= ? , sin B = 150
make b the subject formula;
8/sin15= b/sin 150
b= 8 × sin 150/sin 15
b= 80cm
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Select the correct answer.
Consider this expression.
x-4
2(x+4)
For which product or quotient is this expression the simplest form?
O A.
B.
O C.
O D.
2x+8
x²16
x²16
2x+8
2x+8
x²16
x²16
2x+8
÷
÷
.
.
x² + 8x + 16
x +4
x +4
x² + 8x + 16
x² + 8x + 16
x + 4
x+4
x² + 8x + 16
The rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16
Multiplying rational expressionsRational expressions are written in the form a/b where a and b are integers.
According to the question, we need to determine the expression that is equal to x-4/2(x+4)
From the fourth option;
x²-16/2x+8 * x+4/x²+8x+16
Factorize the quadratic part to have;
x²-16/2x+8 * x²+8x+16/x+4
(x+4)(x-4)/2(x+4) * x+4/(x+4)^2
Cancel out the common expression to have;
x-4 * 1/2(x+4)
x-4/2(x+4)
Hence the rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16
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Andre says that [tex]log_10(55)=1.5[/tex] because 55 is halfway between 10 and 100. Do you agree with Andre? Explain your reasoning.
I know that answer is false, but I don't know how to explain!!
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllllllll} \log_{\underline{10}}(10)=1&\implies &\underline{10}^1=10 ~~ \checkmark\\\\ \log_{10}(100)=2&\implies &10^2=100~~ \checkmark\\\\ \log_{10}(55)=1.5&\implies &10^{1.5}=55\implies 10^{\frac{3}{2}}=55\implies \sqrt[2]{10^3}=55\\\\ &&\sqrt{1000}\ne 55 ~~ \bigotimes \end{array}[/tex]
increments over the exponent, are not directly proportional to increments on the resulting values, namely the half-way from 10² and 10⁴ is not 10³, because 10⁴ is 100 times 10², and 10³ is simply 10 times 10².
Can someone help me out? :) The answer choices are:
A) 20.0
B) 21.2
C) 22.4
D) 23.6
Answer:
20.0
Step-by-step explanation:
We can use the distance formula, d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] to find the length of three sides separately.
AB = [tex]\sqrt{(-4+2) ^{2} +(1-3}) ^{2}}[/tex] = [tex]\sqrt{8}[/tex]
BC = [tex]\sqrt{(-2-3) ^{2} +(3+4) ^{2}}[/tex] = [tex]\sqrt{74}[/tex]
CA = [tex]\sqrt{(3+4) ^{2} +(-4-1) ^{2}}[/tex] = [tex]\sqrt{74}[/tex]
Perimeter = [tex]\sqrt{74}[/tex] + [tex]\sqrt{8}[/tex] + [tex]\sqrt{74}[/tex] = 20.0330776588 units
Answer:
Step-by-step explanation:
If you flipped two coins simultaneously, for a total of 24 times, how many times, on average, would you expect to get a head and a tail?
When two coins are flipped simultaneously 24 times, on average 12 times we will get a head and a tail.
For given question,
When two coins are tossed simultaneously, the sample space is as follows:
S = { HH, HT, TH, TT} where H denotes Head and T denotes tail.
Using the formula of probability,
P = Number of favorable outcomes/total number of outcomes,
we get,
P(HT) = 1/4
and
P(TH) = 1/4
We know that the occurrence of two mutually exclusive events is the sum of their individual probabilities.
So, P(Head on one and Tail on other)
= P(HT) + P(TH)
= 1/4 + 1/4
= 2/4
= 1/2
= 0.5
So, when two coins flipped simultaneously, the probability of flipping 2 coins and getting a head and a tail is 0.5
In this question, we need to find the number of times getting a head and a tail when two coins are flipped simultaneously 24 times
= 0.5 × 24
= 12
Therefore, When two coins are flipped simultaneously 24 times, on average 12 times we will get a head and a tail.
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PLLLLLEASE T_T PLLLEASE
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
let's solve ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{4}{y - 6} + \cfrac{5}{y + 3} = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{4(y + 3) + 5(y - 6)}{(y - 6)(y + 3)} = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{4y + 12 + 5y - 30}{ {y}^{2} + 3y - 6y - 18 } = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{9y - 18}{ {y}^{2} - 3y - 18 } = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: 9y - 18 = 7y - 4[/tex]
[ denominator is same, so numerator must have same value to be equal ]
[tex]\qquad \sf \dashrightarrow \: 9y - 7y = - 4 + 18[/tex]
[tex]\qquad \sf \dashrightarrow \: 2y = 14[/tex]
[tex]\qquad \sf \dashrightarrow \: y = 7[/tex]
Sketch The Graphs:
y = -1/3x -2
Answer:
Step-by-step explanation:
The graph of the straight line [tex]y = -\frac{1}{3}x -2[/tex] is plotted. The graph is shown below.
A straight line is of the form y = mx + c, where m is the slope and c is the y-intercept.
To plot the given straight line [tex]y = -\frac{1}{3}x -2[/tex], follow the following steps:
Step 1: Substitute x = 0 in the given equation to obtain the point where the line intersects the y-axis.
y = 0 - 2
y = -2
The point at the y-axis is (0, -2).
Step 2: Substitute y = 0 in the given equation to obtain the point where the line intersects the x-axis.
[tex]0 = -\frac{1}{3}x -2\\x = -6[/tex]
The point at the x-axis is (-6, 0).
Step 3: Draw a straight line passing through both points.
Thus, the straight line [tex]y = -\frac{1}{3}x -2[/tex] is plotted.
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Coplanar circles that have the same center, but not necessarily the congruent radii are called?
Coplanar circles that have the same center, but not necessarily the congruent radii are called concentric circles.
How to complete the blank?From the question, we have the following statements:
The circles are coplanar i.e. they are on the same planeThey have the same circleThe radii of the circles are differentAs a general rule, circles that have the above features are referred to as concentric circles.
This is so because concentric circles have the same center, and they do not intersect
Hence, coplanar circles that have the same center, but not necessarily the congruent radii are called concentric circles.
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find the square roots of each of the following number
1: 81
2: 100
Multiply 9 with 9, and we get:
9 × 9 = 81
Multiply 10 with 10, and we get:
10 × 10 = 100
We get the final result as:
9²10²Hope this helps :)
creating holes in the sand to fill the varied buckets is an example of an inverse relationship
true or false
Answer:
True
Step-by-step explanation:
You are taking away sand from the ground and adding sand to the bucket. There is less sand on the ground and more in the bucket making it inverse.
What is the slope of the line that passes through the points (9, 2) and
(9,27)? Write your answer in simplest form.
Answer:
Slope (m) = infinity
Step-by-step explanation:
Given points:
⇒ (9, 2) and (9, 27)
In order to find the slope of these points, we must use the slope formula.
So the formula is ⇒ y₂ - y₁ / x₂ - x₁
Plug in the given points:
⇒ 27 - 2 / 9 - 9
Solve both the top and bottom (numerator and denominator):
⇒ 25 / 0
Divide:
⇒ Undefined.
(Anything divided by zero is undefined).
use the fact that there are 2pi radians in each circle to find another angle, smaller than 2pi, that is equivalent to 17pi/6. with detailed steps pleasee
The equivalent angle in the interval [0, 2pi] is 5pi/6.
How to find the equivalent angle?
Remember that for any given angle θ in radians, we define a family coterminal or equivalent angles as:
A = θ + n*(2pi)
Where n is a whole number.
Now we want to find an angle equivalent to 17pi/6 that is on the range between 0 and 2pi.
Then we can write:
A = 17pi/6 + n*(2pi)
If we use n = -1, then we get:
A = 17pi/6 - 2pi = 17pi/6 - 12pi/6 = 5pi/6
This is the equivalent angle in the desired range.
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We can fill a certain barrel with water if we use water from 6 small pitchers, 3 medium pitchers, and one large pitcher, or from 2 small pitchers, 1 medium pitcher, and 3 large pitchers. If we use only large pitchers of water, how many of them do we need to fill the barrel?
Answer:
Solution Given:
let pitcher which is small be S medium be M and large be L and barrel be B.
By question
6S+3M+1L= 1B...... eq. 1
2S+1M+3L=1B.......eq. 2
The difference in 2L from the first to the second is 4S and 2M
Therefore, each L=2S+M
In equation 2
2S+1M+3L=1B
replacing 2S +1M by L,we get
L+3L=1B
4L=1B
Therefore, 4 large pitcher is required
Answer:
4 large pitchers
Step-by-step explanation:
Define the variables:
Let x = volume of a small pitcherLet y = volume of a medium pitcherLet z = volume of a large pitcherLet b = volume of a barrelCreate two equations with the given information and the defined variables.
Equation 1
If the barrel can be filled with 6 small pitchers, 3 medium pitchers and 1 large pitchers:
⇒ 6x + 3y + z = b
Equation 2
If the barrel can be filled with 2 small pitchers, 1 medium pitcher and 3 large pitchers:
⇒ 2x + y + 3z = b
Substitute Equation 2 into Equation 1
⇒ 6x + 3y + z = 2x + y + 3z
Subtract 6x from both sides:
⇒ 3y + z = -4x + y + 3z
Subtract y from both sides:
⇒ 2y + z = -4x + 3z
Subtract z from both sides:
⇒ 2y = -4x + 2z
Divide both sides by 2:
⇒ y = -2x + z
Substitute the found expression for y into Equation 1:
⇒ 6x + 3(-2x + z) + z = b
⇒ 6x - 6x + 3z + z = b
⇒ 4z = b
Therefore, 4 large pitchers are needed to fill the barrel.
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1. Ellie has 2/8 pound of cheese. She used 1/2 of the cheese to make tacos. Since there are 16 ounces in one pound, how many ounces of cheese does Ellie use to make tacos?
The ounces of cheese Ellie uses to make tacos is 2
What is a unitary method?
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Calculation :
1 pound = 16 ounces
Total cheese Ellie has = [tex]\frac{2}{8}[/tex] pound
Cheese required to make tacos = [tex]\frac{2}{8}[/tex]×[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{8}[/tex] pounds
Ounces of cheese required to make cheese are [tex]\frac{1}{8}[/tex] × 16 = 2 ounces
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Given MTS and SQP, find sq
From the given similar triangles we can conclude that the length of Side SQ is; 4
How to solve similar triangles?
We are given that;
PQ is parallel and congruent to MT.
Now, from the concept of similar triangles , we can say that;
PS/TS = QS/MS
From the given triangle we see that;
PS = 3 - 2x
QS = 6x - 1
MS = 30
TS = 10
Thus;
(3 - 2x)/10 = (6x - 1)/30
Cross multiply to get;
3(3 - 2x) = 6x - 1
9 - 6x = 6x - 1
Rearranging gives;
6x + 6x = 9 + 1
12x = 10
x = 10/12
x = 5/6
Thus;
SQ = 6(5/6) - 1
SQ = 4
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5. The grid shows how many eggs Ms. Benton bought.
The shaded boxes represent the number of eggs she
used to make the cookies. What percent and fraction
of the eggs bought were not used to make the cookies?
Show your work in the space below. Remember to
check your solution.
Answer:
You can count how many boxes that are not shaded to find how many eggs were not used, but that's to find out the fraction
Step-by-step explanation:
Count the boxes total in the grid. then count the number of boxes were not shaded. the number of total boxes is your denominator, and the number of boxes thar aren't shaded is your numerator.
I think...
Which of the following is equivalent to the quotient below?
√135/√3
A. 5√3
B. √45/3
C. 3√5
D. 3√15
The answer is C. 3√5.
√135/√3√45√3² × 53√5sariah has just begun training for a half-marathon, which is 13.1 miles. since she was on vacation, she started the training program later than the rest of her running club. There are 6 weeks of training runs remaining before the race.
In her first week of training, Sariah ran 3 miles. She ran 4.5 miles the second week and 6 miles the third week. If she continues to increase the length of her runs the same way, will there be enough time left in the train program for her to get up to half-marathon distance?
Describe how you would solve this problem using Polya’s four-step problem-solving method. Complete each task as part of your response. Be sure to number task 1-task 4 so that your instructor can tell which part you are answering.
1. understand the problem
task 1: read the problem and restate in your own words what the question asks.
2. formulate a plan
task 2: identify the model you would use to represent the problem and explain why you chose the model.
3. implement the plan
task 3: solve the problem and state your answer.
4. review the results
task 4: explain your problem-solving process and how you know your answer is correct.
There would not be enough time to reach the half marathon distance.
Would there be enough time to reach the half marathon distance?The distance run in a week can be represented with a linear equation. A linear equation is an equation that has a single variable raised to the power of 1.
The linear equation that would be used to represent the distance run would be in the form:
Miles run in a week = miles run the previous week - increase in miles
Increase in miles = 6 - 4.5 = 1.5 miles
Miles run in the fourth week = 1.5 + 6 = 7.5 miles
Miles run in the fifth week = 7.5 miles + 1.5 miles = 9 miles
Miles run in the sixth week = 9 + 1.5 = 10.5 miles
There would not be enough time to reach the half marathon distance because in the sixth week she would be able to run 10.50 miles
To learn more about linear functions, please check: https://brainly.com/question/26434260
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A steel hex nut has two regular hexagonal bases and a cylindrical hole with a diameter of 1.6 centimeters through the middle. the apothem of the hexagon is 2 centimeters. a cylinder is cut out of the middle of a hexagonal prism. the hexagon has an apothem with a length of 2 centimeters and base side lengths of 2.3 centimeters. the prism has a height of 2 centimeters. the cylinder has a diameter of 1.6 centimeters. the equation for the area of a regular hexagon = one-half (apothem) (perimeter). what is the volume of metal in the hex nut, to the nearest tenth? use 3.14 for π.
Subtracting the volume of the cylinder from the volume of the prism, the volume of metal in the hex nut to the nearest tenth exists [tex]$$23.6 cm^3[/tex]
How to estimate the volume of metal in the hex nut?Diameter of the cylinder be d = 1.6 cm
Apothem of the hexagon be a = 2 cm
Thickness of the steel hex nut be t = 2 cm
Volume of the prism be [tex]V_p[/tex]
Volume of the cylinder be [tex]V_c[/tex]
Volume of metal in the hex nut,
[tex]$$V = V_p - V_c[/tex]
To estimate the volume of a prism,
[tex]$$V_p = A_b h[/tex]
Ab = n L a / 2
Number of the sides, n = 6
The side of the hexagon be L
Height of the prism, h = t = 2 cm
Central angle in the hexagon, A = 360°/n
A = 360°/6 = 60°
[tex]$tan (\frac{A}{2} )=(\frac{L/2}{a})[/tex]
simplifying the value of L, we get
[tex]$tan (\frac{60}{2} )=(\frac{L/2}{2})[/tex]
[tex]$tan 30}=(\frac{L/2}{2})[/tex]
[tex]$tan (\frac{\sqrt{3}}{3} )=(\frac{L/2}{2})[/tex]
Solving for L/2:
[tex]$\frac{2 \sqrt{3}}{3} =\frac{L}{2}[/tex]
Solving the value of L, we get
[tex]$2\frac{2 \sqrt{3}}{3} =L[/tex]
[tex]$\frac{4 \sqrt{3}}{3} =L[/tex]
[tex]$L=4 \sqrt{3}/3 cm[/tex]
Ab = n L a / 2
Substitute the values in the above equation, we get
[tex]$A_b=\frac{6 (4 \sqrt{3}/3)(2)}{2}[/tex]
[tex]$$A_b=24 \sqrt{3}/3 $$cm^2[/tex]
[tex]$A_b=8 \sqrt{3} cm^2[/tex]
[tex]V_p = A_b h[/tex]
substitute the values in the above equation, we get
[tex]$V_p=(8 \sqrt{3})(2)[/tex]
[tex]$V_p=16 \sqrt{3} cm^3[/tex]
[tex]$$V_p=16 (1.732) cm^3[/tex]
[tex]$$V_p=27.712 cm^3[/tex]
To estimate the volume of cylinder,
[tex]$V_c[/tex] = (π[tex]d^2[/tex]/4) h
Here, π = 3.14 and d = 1.6 cm
Height of the cylinder, h = t = 2 cm
substitute the values in the above equation, we get
[tex]$V_c=[3.14 (1.6) / 4] (2)[/tex]
[tex]$V_c=[3.14 (2.56) / 4] (2)[/tex]
[tex]$V_c=(2.0096) (2)[/tex]
[tex]$$V_c=4.019 cm^3[/tex]
Substitute the values in the equation, we get
[tex]$$V=V_p-V_c[/tex]
[tex]$$V=27.712 - 4.019[/tex]
[tex]$$V=23.693 cm^3[/tex]
[tex]$$V=23.6 cm^3[/tex]
Therefore, the volume of metal in the hex nut, to the nearest tenth exists [tex]$$23.6 cm^3[/tex].
To learn more about volume of cylinder and prism refer to:
https://brainly.com/question/12669337
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