The range of a function are the dependent variables for which the function exists. The range of the function will be y ≥ 5
Range of a function
The range of a function are the dependent variables for which the function exists
Given the function below;
f(x) = √x+7 + 5
The function can only exist for values less than or equal to -7 that is x ≤ -7.
Substitute
f(-7) = √-7+7 + 5
f(-7) = 5
The range of the function will be y ≥ 5
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Point X is the incenter of ΔABC.
Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X. Lines are drawn from point X to the sides of the triangle to form right angles. Line segments X F, X G, and X E are formed.
If EX = 4z + 1, XF = 2z + 7, and mABC = 44°, find the following measures.
GX =
mABX = °
The measures of GX = 13
The measures of [tex]\angle ABX=22^0[/tex]
EX = 4z + 1 and XF = 2z + 7
Take EX and XF equal time each other and then solve for z and then you will get GX because EX = XF = GX are congruent.
EX = XF
What is congruent?
Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
4z + 1 = 2z + 7
2z = 6
z = 3
As, EX = XF = GX
EX = 4(3) + 1
EX = 13
Therefore, GX = 13 ------ ( EX = XF = GX )
To find the angle ABX, divide the angle ABC by 2 you will get
[tex]\angle ABX=22^0[/tex]
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Answer: 13, 22°
Step-by-step explanation: Trust Me!
Answer is correct on Edge. Good Luck! :)
GX = 13
mABX = 22 °
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.
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]
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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30-60-90 Angle Triangle- Geometry
Answer:
perimeter = 42 units
Step-by-step explanation:
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!
solve this trigonometry question too, please by an easy method.
Answer:
proof given below
Step-by-step explanation:
Combine the fractions by making the denominators the same:
[tex]\dfrac{\sin \theta}{1+ \cos \theta}+\dfrac{1+ \cos \theta}{ \sin \theta}[/tex]
[tex]=\dfrac{\sin \theta}{1+ \cos \theta} \cdot \dfrac{\sin \theta}{\sin \theta}+\dfrac{1+ \cos \theta}{ \sin \theta} \cdot \dfrac{1+ \cos \theta}{1+ \cos \theta}[/tex]
[tex]=\dfrac{\sin \theta(\sin \theta)}{\sin \theta(1+ \cos \theta)}+\dfrac{(1+ \cos \theta)(1+ \cos \theta)}{\sin \theta(1+ \cos \theta)}[/tex]
[tex]= \dfrac{\sin^2 \theta}{\sin \theta(1+ \cos \theta)} +\dfrac{1+2 \cos \theta + \cos^2 \theta}{\sin \theta(1+ \cos \theta)}[/tex]
[tex]= \dfrac{\sin^2 \theta+ \cos^2 \theta+1+2 \cos \theta }{\sin \theta(1+ \cos \theta)}[/tex]
Use the trigonometric identity [tex]\sin^2 \theta + \cos^2 \theta=1[/tex] :
[tex]= \dfrac{1+1+2 \cos \theta}{\sin \theta(1+ \cos \theta)}[/tex]
[tex]= \dfrac{2+2 \cos \theta}{\sin \theta(1+ \cos \theta)}[/tex]
Factor out 2 from the numerator:
[tex]= \dfrac{2(1+ \cos \theta)}{\sin \theta(1+ \cos \theta)}[/tex]
Cancel the common factor:
[tex]= \dfrac{2}{\sin \theta}[/tex]
[tex]\textsf{Use the identity} \quad\csc \theta=\dfrac{1}{\sin \theta}:[/tex]
[tex]=2 \csc \theta[/tex]
Hence proved.
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Step-by-step explanation:
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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:
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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]
20points
please come help me
write an exponential function that includes the following given pair of points.
(1,5) and (2,25)
Answer:
[tex]y=5^x[/tex]
Step-by-step explanation:
[tex]y=a*b^x\\(1,5)=5=a*b^1 \implies(1)\\(2,25)=25=a*b^2\implies(2)\\(2)\div(1)=\frac{25}{5} =\frac{a*b^2}{a*b^1} \\5=b[/tex]
[tex](1)=5=a*5\implies a=1 y=5^x\implies y=5^x[/tex]
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 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
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:
The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral
The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral is 90° counterclockwise rotation about point A followed by the reflection across y axis and a translation 20 units down.
What is transformation?It should be noted that a transformation simply illustrates the change in shape.
In this case, the sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral is 90° counterclockwise rotation about point A.
This will then be followed by the reflection across y axis and a translation 20 units down.
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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]
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 :)
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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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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A 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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the complete transformation is Rk, where k is the line with equation
The complete transformation is Rk, where k is the line with equation x = 2
How to complete the transformation?The complete question is added as an attachment
From the attached graph, we can see that the triangle and its image have a common vertex at C.
This means that the triangle is reflected across a vertical line that passes through point C.
The coordinate of C is:
C = (2, -2)
The vertical line passes through the x-coordinate.
So, we have:
x = 2
Hence, the complete statement is:
The complete transformation is Rk, where k is the line with equation x = 2
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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 with this question.
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
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.
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!
How many points? Help me please:)
Answer:
187 Points
Step-by-step explanation:
Total ratio units = 17 + 14 = 31 units
Total they scored = 341 points
Therefore total units = 31 = 341 points
31 units = 341 points
1 unit = (341/31) points
1 unit = 11 points
Nina scored 17 units of the total points
17 units = (17 x 11) points
= 187 points
graph
y=x-1
y=-2x+5
what is the solution?
Answer:
(x,y) --> (2,1)
Step-by-step explanation:
hope this helps