Answer:
62
Step-by-step explanation:
1. To find the total area, we must find the area of the three individual gardens and sum them together
2. Since the gardens are square, the area is equal to the side length squared
3. Therefore, square the sides and sum:
3^2 = 9
7^2 = 49
2^2 = 4
4+9+49 = 62
Triangle A E C is shown. Line segment B D is drawn near point C to form triangle B D C.
Which piece of additional information can be used to prove △CEA ~ △CDB?
∠BDC and ∠AED are right angles
AE ≅ ED
△BDC is a right triangle
∠DBC ≅ ∠DCB
∠BDC and ∠AED are right angles, is a piece of additional information is appropriate to prove △ CEA ~ △ CDB
Triangle AEC is shown. Line segment B, D is drawn near point C to form triangle BDC.
Similar triangles, are those triangles which have similar properties,i.e. angles and proportionality of sides.
Image is attached below,
as shown in figure
∡ACE = ∡BCD ( common angle )
∡AED = ∡BDC ( since AE and BD are perpendicular to same line EC and make right angles as E and C)
∡EAC =- ∡DBC ( corresponding angles because AE and BD are parallel lines)
Thus, △CEA ~ △CDB , because of the two perpendiculars AE and BD.
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Answer:
A
Step-by-step explanation:
In a group of 26 students, 4 study both art and biology. 5 study biology but not art. 5 study neither subject. given that a randomly selected student studies art, what is the probability the student studies art and biology?
[tex]\huge\boxed{25\%}[/tex]
We need to find the number of students that study art first. This includes the students who study both art and biology (4) and the students who study art but not biology.
We know the counts for every category except for "art but not biology", so we can use subtraction.
[tex]26-4-5-5=12[/tex]
This means that 12 students study art but not biology, which combines with the 4 who study both subjects to give us 16 art-studying students.
Now, we just need to find the probability that a student studies both subjects (4 students) given that they study art (16 students).
This is simple division.
[tex]4/16=0.25=25\%[/tex]
ritas total bill at a restaurant was 25.00 including tax. if she left a tip of 20% of the total bill, what was the amount of the tip
Answer:
She left a $2 tip
Step-by-step explanation:
0.2*25 = 5
30-60-90 Angle Triangle- Geometry
Answer:
perimeter = 42 units
Step-by-step explanation:
The end of month balances of college students is listed in the following chart. 25 37 43 55 57 68 72 74 87 123 125 127 141 149 185 203 215 234 234 252 279 302 303 321 327 350 358 404 425 440 489 489 503 521 608 703 712 758 863 900 Your first interval has a frequency of 14 and a total of 40, what is the value of the Relative Frequency Distribution
The value of the relative frequency distribution of the first interval, having a frequency of 14, and the total frequency given is 40, is 0.35.
In a Relative Frequency Distribution, we list how often a data value appears and scale it using the total frequency.
The sum of Relative Frequencies adds to 1.
In the question, we are informed that the first interval has a frequency of 14.
This implies that the data appears 14 times in the first interval.
Also, we are told that the total frequency is 40.
Thus, the relative frequency can be calculated as the ratio of the frequency of the interval to the total frequency.
Therefore, Relative frequency = 14/40 = 0.35.
Thus, the value of the relative frequency distribution of the first interval, having a frequency of 14, and the total frequency given is 40, is 0.35.
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What is the root of the polynomial equation x (x minus 2) (x 3) = 18? use a graphing calculator and a system of equations.
The root of the polynomial equation x (x-2) (x + 3) = 18 is x = 3.
Concept: An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
Given:
x (x-2) (x + 3) = 18
Divide both sides of the equation by x:
x (x-2) (x + 3) / x = 18 / x
(x-2) (x) + 3) = 18 / x
You can use the following simultaneous equations.
(1) y = (x-2) (x + 3)
(2) y = 18 / x
Using a graphing calculator, we get:
x = 3, y = 6 → point = (x, y) = (3,6)
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I Need Help Please And Thank You.
Answer:
8x+55y ≤ 184
Step-by-step explanation:
8x: The x in 8x signifies the amount of books you can buy. So let's say you want to buy 4 books then x would be 4 and 8x would be equivalent to 42.
55y: The y in 55y signifies the amount of video games you can buy. So let's say you want to buy 2 video games then y would be 2 and 55y would be equivalent to 110.
≤: We're using this sign because you can spend a maximum of 184 dollars. Meaning that the amount you spend (which is the 8x+55y) has to be less than or equal to 184 dollars.
184: The amount of money you are able to spend total.
Hope that helps! If you have any questions feel free to ask me :)
PLEASE HELP
The graph of g(x) is shown.
The graph has...
#1.
a. the same horizontal asymptote as function g
b. a horizontal asymptote at y = 5
c. a horizontal asymptote at y = 8
#2. The graph has...
a. the same vertical asymptote as function g
b. a vertical asymptote at x = -7
c. a vertical asymptote at x = -5
d. a vertical asymptote at x = 3
On the given graph, we can see that we have:
Horizontal asymptote at y = 3Vertical asymptote at x = -2The correct option would be a in both cases.
What can we conclude about the graph of g(x)?We want to study the asymptotes of the graph
If we look at the graph, we can see that the horizontal asymptote (denoted by the horizontal dashed line) is at y = 3.
the graph has a horizontal asymptote (or two actually) at y = 3.
For the vertical asymptote we just look at the vertical dashed line, it is at x = -2
Notice that none of these coincides with the options, so the only options that can be correct (depending on the graph of g(x), which is not shown) are option "a" in both cases.
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I need help with this question.
what value is equivalent to the expression?
Answer: D. -0.002
Step-by-step explanation: You always do the stuff in parenthesis first (P.E.M.D.A.S.). -1/6 is about -0.167. Next you do -0.167 to the fourth power, which is -0.0007777963. Finally, you multiply that number and 2. And BOOM: you get -0.0015555926, which rounds up to -0.002!
a man is walking a 300 foot long field at the same time his daughter is walking towards him from the opposite end . The man is walking 9 feet per second and the daughter is moving 6 feet per second . How many seconds will it take them to meet somewhere in the middle?
Answer:20ft
Step-by-step explanation:Because you add the numbers up 9 and 6 you get 15 so 300/15=20
20x15 equals 300 so it goes both ways
Complete the statements about simplifying this expression: (xy^3/yz^2)(z^3/y^2x^2)
Hence, the variable y can be entirely eliminated using by applying the identity property of elimination
the numerator of the rational expression in the simplest form is z
the denominator of the rational expression in the simplest form is x
What is an expression?expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
How to solve?we have,
[tex](\frac{xy^3}{yz^2} )(\frac{z^3}{y^2x^2} )[/tex]
on simplifying,
we get. [tex]\frac{z}{x}[/tex]
Hence, the variable y can be entirely eliminated using by applying the identity property of elimination
the numerator of the rational expression in the simplest form is z
the denominator of the rational expression in the simplest form is x
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Point P is the center of the circle that is circumscribed around the triangle.
A triangle is inscribed within a circle. Point P is at the center of the circle.
What does point P represent with regard to the triangle?
the point of concurrency of the altitudes
the point of concurrency of the angle bisectors
the point of concurrency of the medians
the point of concurrency of the perpendicular bisectors
The point of concurrency of the perpendicular bisectors represents the point P with regard to the triangle. so option D is correct.
What is altitude?An altitude is a line that is perpendicular to a side and passes through the opposite vertex.
Point P is the center of the circle that is circumscribed around the triangle.
Triangle is inscribed within a circle. Point P is at the center of the circle.
The point P is the circumcenter of the triangle and the point is also equidistant from all the vertices of the triangle.
The one that represents the point P with regard to the triangle.
The point of concurrency of the perpendicular bisectors
Option (D) is correct.
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The point of concurrency of the perpendicular bisectors represents the point P with regard to the triangle. so option D is correct.
What is altitude?
An altitude is a line that is perpendicular to a side and passes through the opposite vertex.
Point P is the center of the circle that is circumscribed around the triangle.
Triangle is inscribed within a circle. Point P is at the center of the circle.
The point P is the circumcenter of the triangle and the point is also equidistant from all the vertices of the triangle.
The one that represents the point P with regard to the triangle.
The point of concurrency of the perpendicular bisectors
Option (D) is correct.
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What is the coefficient of X in the expression x/2+y+z
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
note that [tex]\frac{x}{2}[/tex] represents [tex]\frac{1}{2}[/tex] x
so the coefficient of the x- term is [tex]\frac{1}{2}[/tex]
Tien has three employees working for her in Saskatoon. Each employee is paid
minimum wage for an 8 hour day. They are also paid a commission of 12% on all sales
they make. If the three employees made sales of $785.96, $452.87, and $616.42, how
much must Tien pay in total for the day
The addition is one of the four fundamental mathematical operations. The total wage that Titan needs to pay is $414.63.
What is Addition?The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
Given Each employee is paid a minimum wage of $8/hour for an 8-hour day. They are also paid a commission of 12% on all sales they make. Therefore, the expression for the minimum wage can be written as,
Pay for an employee = (8x8) + 0.12(Sales made) = $64 + 0.12(Sales made)
Pay of the first employee = $64 + 0.12($785.96) = $158.32
Pay of the second employee = $64 + 0.12($452.87) = $118.34
Pay of the third employee = $64 + 0.12($616.42) = $137.97
The total wage that is needed to be paid for the day i,
Total = $158.32 + $118.34 + $137.97 = $414.63
Hence, The total wage that Titan needs to pay is $414.63.
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The length of one of two chords of a circle is 12 cm. If the chords are 6 cm and 7 cm respectively away from the centre of the circle, calculate the length of the second chord...
Please with explanation
Answer:
2√23 cm or 9.59 cm to the nearest hundredth
Step-by-step explanation:
The 12 cm chord is 6 cm away from the centre and the other chord is 7 cm away from the centre.
If we draw 4 radii from the ends of the 2 chords to the centre and 2 lines perpendicular from the centre to the 2 chords we have 2 pairs of congruent right triangles.
So by Pythagoras:
r^2 = 6^2 + 6^2 ( the given chord)
r^2 = 7^2 + x^2 where x is 1/2 * length of the second chord.
Therefore:
7^2 + x^2 = 6^2 + 6^2
x^2 = 36+ 36 - 49 = 23
x = √23
and length second chord = 2√23.
find the value of 7 + 15 + 23 +...+ 767 + 775 + 783?
Answer:
The value of the given sum is 38710===============
GivenThe sum:
7 + 15 + 23 + ... + 767 + 775 + 783We can notice that:
Subsequence terms have the difference of 8,The first term is 7,The last term is 783.Since the difference between subsequence terms is same, the terms form an arithmetic progression.
Use the nth term equation to find the number of terms:
aₙ = a₁ + (n - 1)dUse the given values and find n:
783 = 7 + (n - 1)*88(n - 1) = 776n - 1 = 776/8n - 1 = 97n = 98Now use the equation for sum of the first n terms of AP:
Sₙ = (a₁ + aₙ)*n/2Substitute the values and calculate the sum:
S₉₈ = (7 + 783)*98/2 = 790*49 = 38710A kite flies in the sky with a thread of 68m and makes an angle theta. If tan theta = 15/8, the the height of the kite above the ground is ?
Answer:
60 meter
Explanation:
[tex]\begin{tabular}{|c|c|c|c|} \cline{1-2} \multicolumn{2}{|c|}{\bf {SOH CAH TOA Formula's}} \\ \cline{1-2} \cline{1-2} \rm{sine rule} & sin(\theta) \sf = opposite/hypotenuse \\ \cline{1-2} \rm{cosine rule} & cos(\theta) \sf = adjacent/hypotenuse \\\cline{1-2} \rm{tan rule} & tan(\theta) \sf = opposite/adjacent \\ \cline{1-2}\end{tabular}[/tex]
Given following:
hypotenuse: 68 meter
---
tan(θ) ratio = opposite/adjacent = 15/8
---
To find ratio of hypotenuse (use Pythagoras theorem):
(hypotenuse)² = (adjacent)² + (opposite)²
(h)² = (8)² + (15)²
h² = 289
h = √289 = 17
The height of the kite above ground is the opposite size.
[tex]\sf real \ size = ratio \ size[/tex]
[tex]\sf \dfrac{height \ above \ ground}{hypotenuse} = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\sf \dfrac{height \ above \ ground}{68} = \dfrac{15}{17}[/tex]
[tex]\sf {height \ above \ ground}= \dfrac{68(15)}{17}[/tex]
[tex]\sf {height \ above \ ground}= 60 \ m[/tex]
Answer:
60 m
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)The given scenario can be modeled as a right triangle (see attached diagram) where:
θ = angle the thread makes with the groundhypotenuse = thread of the kiteside opposite the angle = the height of the kite above the groundAs we have been given the hypotenuse (thread) and the angle θ, and need to find the height (side opposite the angle), we can use the sine trigonometric ratio.
The angle θ has been given as a tan trigonometric ratio.
[tex]\sf \textsf{Therefore, if }\tan \theta=\dfrac{15}{8} \textsf{ then } \cos \theta=\dfrac{8}{17} \textsf{ and } \sin \theta = \dfrac{15}{17}[/tex]
To calculate the height of the kite above the ground, substitute the values into the sine ratio formula and solve for height:
[tex]\implies \sin \theta=\sf \dfrac{height}{thread}[/tex]
[tex]\implies \sf \dfrac{15}{17}=\sf \dfrac{height}{68}[/tex]
[tex]\implies \sf height=\dfrac{15}{17} \cdot 68[/tex]
[tex]\implies \sf height=\dfrac{1020}{17}[/tex]
[tex]\implies \sf height = 60 \:m[/tex]
Therefore, the height of the kite above the ground is 60 m.
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Drag the tiles to the correct boxes to complete the pairs
68% of the data lies within one standard deviation from the mean
95% of the data lies within two standard deviation from the mean
99.7% of the data lies within three standard deviation from the mean
What is empirical rule?The empirical rule states that for a normal distribution, 68% of the data lies within one standard deviation from the mean, 95% of the data lies within two standard deviation from the mean and 99.7% of the data lies within three standard deviation from the mean
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Madison and Aiden share a reward of $36 in a ratio of 1:5. What fraction of the total reward does Madison get?
Answer:
1/6
Explanation:
$36 in 1:5
so, the total amount of shares is 6 (1+5)
36 / 6 = 6
$6 per share
shared in the ratio of 1:5
5 x 6 = 30
1:5
M:A
$6:$30
Madison gets $6. Or, 6/36 of the total (which, simplified, is 1/6)
Hope this makes sense!
No Solutions
5x - 2x + 7 - x = _x + _
Answer:
2x+7
Step-by-step explanation:
To Simplify an Expression , we combine Like-Terms
So for our Question , we have Terms with x and Constant Term
Combine Terms with x : 5x-2x-x=2x
Constant Term : 7
Then 5x-2x+7-x = 2x+7
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathbf{5x - 2x + 7 - x = }[/tex] ________[tex]\mathbf{\ x \ + }[/tex]________
[tex]\huge\textbf{Simplify the left side of the equation, to}\\\huge\textbf{get the result of the right side of the}\\\huge\textbf{equation.}[/tex]
[tex]\huge\textbf{Simplifying the LEFT side:}[/tex]
[tex]\mathbf{5x - 2x + 7 - x}[/tex]
[tex]\mathbf{= 5x - 2x + 7 - 1x}[/tex]
[tex]\huge\textbf{Combine the like terms:}[/tex]
[tex]\mathbf{= (5x - 2x - 1x) + (7)}[/tex]
[tex]\mathbf{= 5x - 2x - 1x + 7}[/tex]
[tex]\mathbf{= 3x - 1x + 7}[/tex]
[tex]\mathbf{= 2x + 7}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{2\mathsf{x} + 7}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]GEOMETRY) the question is on the picture below :)
Answer: 33
Step-by-step explanation:
Angles inscribed in the same arc are congruent, so
[tex]13+4x=-7+8x\\\\20+4x=8x\\\\20=4x\\\\x=5\\\\\implies m\angle CDE=-7+5(8)=33^{\circ}[/tex]
A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 0, 2, 8, 2, 0, negative 2. What are all of the x-intercepts of the continuous function in the table? (0, 8) (–4, 0) (–4, 0), (4, 0) (–4, 0), (0, 8), (4, 0
Answer: (-4,0), (4,0)
Step-by-step explanation:
x-intercepts are when y=0.
graph
y=x-1
y=-2x+5
what is the solution?
Answer:
(x,y) --> (2,1)
Step-by-step explanation:
hope this helps
Eli claims that the product of 6 superscript 5 and 5 superscript negative 3 is 6 squared. which explains whether eli is correct?
Answer:
Eli is incorrect. He added the exponents even though the bases are not the same.
Step-by-step explanation:
6^5 * 5^-3 = 6^2
5^-3 = 1/5^3 = 1/125
6^5 = 7776
7776*1/125 = 7776/125 = 62.2 approximately
Answer:
Eli is incorrect. He added the exponents even though the bases are not the same.
Step-by-step explanation:
Edge
A coordinate plane with a vertical line passing through (negative 3, negative 3), (negative 3, 0) and (negative 3, 3). What is the equation of the graphed line written in standard form? x = –3 y = –3 x + y = –3 x – y = –3
Answer:
x = - 3
Step-by-step explanation:
A vertical line parallel to the y- axis has equation
x = c
where c is the value of the x- coordinates the line passes through
the line passes through (- 3, 0 ) and (- 3, 3 ) with x- coordinates - 3 , then
x = - 3 ← equation of vertical line
The __________ is a measure of dispersion that is used in constructing confidence intervals for the mean and in evaluating research hypotheses.
The standard deviation is a measure of dispersion that is used in constructing confidence intervals for the mean and in evaluating research hypotheses.
In statistics, the same old deviation is a degree of the amount of variation or dispersion of a hard and fast of values. A low well-known deviation suggests that the values tend to be close to the suggested of the set, while an excessive widespread deviation shows that the values are spread out over a much broader range.
It tells you, in common, how some distance every rating lies from the suggestion. In everyday distributions, a high well-known deviation approach that values are typically far from the implied, while a low popular deviation suggests that values are clustered close to the mean.
Fashionable deviation tells you ways to unfold out the statistics is. It is a degree of the way some distance each location cost is from the suggest. In any distribution, about ninety-five% of values may be inside 2 preferred deviations of the suggested.
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Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that both marbles are red.
[tex]|\Omega|=8\cdot7=56\\|A|=2\cdot1=2\\\\P(A)=\dfrac{2}{56}=\dfrac{1}{28}[/tex]
Hello, I know it is kinda late but here's a question.
9 = 4a - 2
What is a?
Worth 15 points!
The solution of the linear equation is a = 11/4.
How to solve the linear equation?Here we have the linear equation:
9 = 4a - 2
We want to solve this for a, so we need to isolate a on one side of the equation.
First, we can add 2 on both sides to get:
9 + 2 = 4a
11 = 4a
Now we can divide both sides by 4 to get:
11/4 = a
The solution of the linear equation is a = 11/4.
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Find the measure of angleq, the smallest angle in a triangle whose sides have lengths 4, 5, and 6. round the measure to the nearest whole degree. 34° 41° 51° 56°
The measure of the ∠Q = 41°
By law of cosines:
a law in trigonometry: the square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.
Which can we stated as:
[tex]{q}^2 = {p}^2 + {r}^2 - 2prcos(Q)\\{4}^2 = {6}^2 + {5}^2 - 2*6*5*cos(Q)\\\\[/tex]
solving equation using normal algebra:
60cos(Q) = 36 + 25 - 16
60 cos(Q) = 45
cos(Q) = 45/60
cos(Q) = 3/4
[tex]Q = {cos}^{-1} (\frac{3}{4})\\[/tex]
Thus, Q = 41°
Hence, the measure of the smallest angle in a triangle whose sides have lengths 4, 5, and 6. ∠Q is 41°.
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