Answer:
38
Step-by-step explanation:
hope it helps good day.
Answer:
38 pencils and pens
Step-by-step explanation:
Given
Cost of pencil= $1.20
Cost of pen= $2.90
Difference in cost
= $2.90 -$1.20
= $1.70
Since she bought an equal number of pens and pencils, the additional amount of money spent on pens is due to the difference in price of a pen as compared to a pencil. Let one pen and one pencil be a set.
Number of sets
= $32.30 ÷$1.70
= 19
Since there are 19 sets,
total number of pencils and pen
= 19(2)
= 38
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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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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Mr. Jenkins was arranging chairs for a school awards assembly. Each row contained 15 chairs. If there were 21 rows. how many chairs had to be arranged?
Answer:
315 chairs
Step-by-step explanation:
This question can instill your quick calculation skills which can be very useful when it comes to event planning.
1 row of chairs = 15 chairs
21 rows of chairs = 15 x 21
= 315 chairs.
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]
30-60-90 Angle Triangle- Geometry
Answer:
perimeter = 42 units
Step-by-step explanation:
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.
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
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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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]
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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Polygon LMNOP was transformed to create polygon L'M'N'O'P'.2 pentagons have identical side lengths and angle measures. The points are labeled with the same letters.
Which angle corresponds to AngleN?
Angle
Angle
Angle
Angle
The Angle that would correspond to Angle N after the transformation is; Angle N'
How to Interpret Transformations?
A polygon is defined as a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.
In the transformation of LMNOP to create polygon L'M'N'O'P', we have that;
L corresponds to L'
M corresponds to M'
N corresponds to N'
O corresponds to O'
P corresponds to P'
Thus, we can conclude that Angle N would correspond to Angle N'
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Find the value of each variable in the diagram given that a ∥ b.
Answer:
v = 130
w = 30
x = 100
y = 25
z = 30
Step-by-step explanation:
Question 1
1 pts
You borrow money to purchase a car. You secure a 5 year loan for $15,000 with an annual percentage
rate of 5%. How much will your monthly payments be?
Answer:
$283.07
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]
where:
PMT = monthly paymentP = loan amounti = monthly interest rate (in decimal form)n = term of the loan (in months)Given:
P = 15000i = 5% / 12 = 0.05 / 12n = 5 years = 60 monthsSubstitute the given values into the formula and solve for PMT:
[tex]\implies \sf PMT=\dfrac{15000\left(\frac{0.05}{12}\right)\left(1+\frac{0.05}{12}\right)^{60}}{\left(1+\frac{0.05}{12}\right)^{60}-1}[/tex]
[tex]\implies \sf PMT=283.0685047...[/tex]
Therefore, the monthly payments will be $283.07.
what multiplication expression could the area model above represent?
A: 8.3 x 19
B: 8.3 x 1.9
C: 83 x 19
D: 8.03 X 19
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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question on the image
Answer:
475.2
Step-by-step explanation:
682 is 1.55 of the original amount so 1.55x=682
682/1.55=440
440*1.08=475.2
For f(x) = 4x + 1 and g(x) = x² – 5, find (f+ g)(x).
Answer:
x^2 + 4x -4
Step-by-step explanation:
Simply combine all the like terms by adding:
x^2 + 0x - 5
0x^2 + 4x +1
_____________
x^2 + 4x - 4
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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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 = 38710graph
y=x-1
y=-2x+5
what is the solution?
Answer:
(x,y) --> (2,1)
Step-by-step explanation:
hope this helps
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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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 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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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 °
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 :)
Given: ABCD is a parallelogram and AC bisects BD.
Prove: AB is congruent to BC.
Let's see
In ∆ABE and ∆CBE
BE=BE(Common side)AE=EC[Diagonals of a parallelogram bisect each other]<AEB=<BEC[90°]So by
SAS congruence the triangles are congruent
AB=BC
ProvedFact:-
It's already given AC is perpendicular to BD
It means diagonals are perpendicular to each otherAccording to general property of rhombus this parallelogram is also a rhombus.
So sides are equal hence AB =BC
I need help with this question.
How to put a starting pay of $500 with 100% increase every month on a graph.
This is the graph I need to use
Answer:
if boo ygdv
Step-by-step explanation:
f bi igfcnkyf f jurf