An item on sale costs 15% of the original price. The original price was $97
Answer:
$14.55
Step-by-step explanation:
In the diagram, ABCDE is a regular pentagon.
(a) Calculate /BAE.
(b) What is the name of the quadrilateral ABCD?
(c)The sides AE and CD are produced to meet at X.
(i) Calculate /EDX.
(ii) What type of quadrilateral is BDXE? Explain your answer.
The shape ABCDE is a regular pentagon with five sides, such that the five sides are congruent
Part A: Calculate ∠BAEThe angle BAE is a vertex angle, and it is calculated using:
BAE = 180 * (n - 2)/n
Where n= 5; i.e. the number of sides.
This gives:
BAE = 180 * (5 - 2)/5
Evaluate
BAE = 108°
Hence, the measure of angle BAE is 108°
Part B: The name of the quadrilateral ABCDWhen the vertices A and B are joined together, the shape becomes a trapezoid.
Hence, the name of the quadrilateral ABCD is a trapezoid.
Part C (i) Calculate ∠EDXSee attachment for the new figure.
From the attached figure, we have:
∠EDX + ∠EDC = 180° ---- the sum of angles on a straight line
Where:
∠EDC = ∠BAE = 108°
So, we have:
∠EDX + 108° = 180°
Subtract 108° from both sides
∠EDX = 72°
Hence, the measure of angle EDX is 72 degrees
Part C (ii) What type of quadrilateral is BDXE?The quadrilateral BDXE is a parallelogram.
This is so because the opposite sides of BDXE are parallel, but not congruent
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What two-dimensional shape is formed by the cross section shown below?
Answer:
I believe rectangle.
Step-by-step explanation:
Someone please help and answer this please
Answer:
1) surface area = 2 · π · r · (r + h)
2) 8x5x6x14x8.94
3) surface area = 2 · π · r · (r + h)
4) 8x14x6
5) 4x4x8
6) 7x8.95x13
7) 3x4x11x3.61 divide by 2
8) 6x6x6 = 36x6 = 216
9) 3x4x10
Step-by-step explanation:
The number of bacteria on your hand increases by 40% every hour. If there were initially 800 bacteria placed on your hand, how much bacteria
will be on your hand after 3 hours?
Answer:
about 2195 bacteria
Step-by-step explanation:
After one hour: 800 * 1.4 = 1120
After two hours: 1120 * 1.4 = 1568
After three hours: 1568 * 1.4 = 2195.2
5x+11x using distributive property
[tex]5x+11x=16x[/tex]
What is Distributive Property?To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Distributive Property:
[tex](5x+10x)+(5x+1x)[/tex]
/ \ / \
[tex](16x)[/tex] [tex](6x)[/tex]
Therfore, by using the distributive property, [tex](5x+10x)+(5x+1x)[/tex], We get [tex]16x[/tex].
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5.7.PS-7
Solve the inequality. Then graph the solutions on a number line.
6< - 3(2x-6)
A. X≥
• B. X >
O C. X <
O D. XS
the answer is a x equal to or greater than
solve by completing the square: x^2+18x+45=0
Answer:
x = -3 , - 15
Step-by-step explanation:
Given:
x² + 18x + 45 = 0
Solve:
[tex]x_{1,\:2}=\frac{-18\pm \sqrt{18^2-4\cdot \:1\cdot \:45}}{2\cdot \:1}[/tex]
Simplify
[tex]-18\pm \sqrt{18^2-4\cdot \:1\cdot \:45=12[/tex]
[tex]x_{1,\:2}=\frac{-18\pm \:12}{2\cdot \:1}[/tex]
Separate the solution
[tex]x_1=\frac{-18+12}{2\cdot \:1},\:x_2=\frac{-18-12}{2\cdot \:1}[/tex]
[tex]x_1=\frac{-18+12}{2\cdot \:1}=-3[/tex]
[tex]x_2=\frac{-18-12}{2\cdot \:1}=-15[/tex]
Thus, the answer are:
[tex]x=-3,\:x=-15[/tex]
Kavinsky
1) lan's new Mercedes cost him $75,000. From the
moment he drives it off the lot, it will depreciate
by 20% each year for the first five years. What will
be the car's value be at the end of five years?
(Round to the nearest whole number.)
Answer: The answer to this is 3000,
Step-by-step explanation:
I think this is the answer because when you find out what 20% of 75000 is, (which is 15000) you can divide 20% by 5 and there is your answer, i hope this helps
what is the distance between -45 and 35
Answer:
10
Step-by-step explanation:
Answer:
81
Step-by-step explanation:
-45 minus 35 is -80 so that's 80 units. and including zero it's 81 units
solve each logarithmic equation. Round your answer to two decimal places.
Teach me this one? I want to work on the next and will submit it once I have it done.
7 log9 (x + 8) = 7
Answer:
[tex]\sf \boxed{\bold{x=1}}[/tex]
Explanation:
[tex]\rightarrow \sf 7 log_9 (x + 8) = 7[/tex]
divide both sides by 7
[tex]\rightarrow \sf \dfrac{7\log _9\left(x+8\right)}{7}=\dfrac{7}{7}[/tex]
simplify the following
[tex]\sf \rightarrow \log _9\left(x+8\right)=1[/tex]
apply log rules [tex]\underline{The \ rule}: \ \bold{log_{b} (a)= c} \ \ \Longrightarrow \sf a = b^c[/tex]
[tex]\sf \rightarrow x+8 = 9^1[/tex]
simplify
[tex]\sf \rightarrow x+8=9[/tex]
subtract both sides by 8
[tex]\sf \rightarrow x=1[/tex]
[tex]\\ \rm\Rrightarrow 7log_9(x+8)=7[/tex]
[tex]\\ \rm\Rrightarrow log_9(x+8)=1[/tex]
[tex]\\ \rm\Rrightarrow x+8=9^1[/tex]
a^1=a[tex]\\ \rm\Rrightarrow x+8=9[/tex]
[tex]\\ \rm\Rrightarrow x=9-8[/tex]
[tex]\\ \rm\Rrightarrow x=1[/tex]
What is the result when the number 44
is increased by 75%?
Answer:
77
Step-by-step explanation:
75% of 44 = 33
33 + 44 = 77
Answer:
77.
Step-by-step explanation:
75% of 44
= 3/4 * 44
= 33
33+44
= 77.
Factorise the following:
A. 4xy-16
B. xy+2xy-x
C. 2x²-18x+12
D. 5xy+20x-9y-36
=4(xy−4)
B. xy+2xy-x3xy−x
=x(3y−1)
C. 2x²-18x+122x²−18x+12
=2(x²−9x+6)
D. 5xy+20x-9y-365xy+20x−9y−36
=(y+4)(5x−9)
A bowling ball has a diameter of 8.5 inches. If it is rolled down a 60-foot bowling lane, how many complete revolutions will it make? Round to the nearest tenth.
Worth 25 points!!
Answer:
27 revolutions
Step-by-step explanation:
Things to remember :
One revolution = distance of circumference coveredcircumference = 2πrdiameter = 2 x radiusSolving
One revolution = 2 x π x d/2 = πdOne revolution = 3.14 x 8.5One revolution = 26.69 inchesNo. of revolutions = Distance / one revolutionNo. of revolutions = 60 x 12 / 26.69No. of revolutions = 720 / 26.69No. of revolutions = 27 revolutionsIn a large company, 45% of the employees wear khaki pants on a daily basis. Which calculation finds the probability of getting less than 40% of employees wearing khaki pants in a random sample of 50 employees
The probability of getting less than 40% of employees wearing khaki pants in a random sample of 50 employees is 0.18.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
In a large company, 45% of the employees wear khaki pants on a daily basis.
40% of employees wearing khaki pants in a random sample of 50 employees
So, 40% of 45% x 50
= [tex]0.40 \times 0.45 \times 50 \\ \\9[/tex]
The probability of getting less than 40% of employees wearing khaki pants in a random sample of 50 employees.
= 9 /50
= 0.18
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whats the y intercept and rate of change ill give 20 pt please help me thank u
Answer:
y-intercept= (0,7) and rate of change=
Step-by-step explanation:
The y-intercept of a graph is the point on the graph where it intersects the y-axis or where x=0. In this case it is (0,7) so that is the y-intercept. The rate of change is equal to y2-y1 divided by x2-x1. Basically, just pick 2 random points on the line and subtract their y coordinates, then subtract their x-coordinates and divide the answers with each other. So, one point is (0,7) and another point is (2,4). Therefore, rate of change is 7-4 divided by 0-2. This gives us a rate of change of -3/2
The area of a circle is 49 pi cm^2 what is the radius of a circle
Answer:
The radius is 7 cm
Step-by-step explanation:
We know the area of a circle is given by
A = pi r^2
49 pi = pi r^2
Divide each side by pi
49 = r^2
Take the square root of each side
sqrt(49) = sqrt(r^2)
7 = r
The radius is 7 cm
Answer:
radius = 7 cm
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( r is the radius )
given A = 49π , then
πr² = 49π ( divide both sides by π )
r² = 49 ( take square root of both sides )
r = [tex]\sqrt{49}[/tex] = 7
help me with this question, please
Answer:
Part 1: [ -4 = -8 ]
Part 2: Inconsistent
Step-by-step explanation:
Part 1
1. Move all terms that don't contain x to the right side:
3x - 6y+6y = -12+6y
= 3x = -12 + 6y
2. Isolate x:
[tex]\frac{3x}{3} = \frac{-12+6y}{3}[/tex]
x = -4 + 2y
3. Substitute the new expression into the original:
-4 + 2y - 2y = -8
4. Simplify:
-4 + 0 = -8
[ -4 = -8 ]
Part 2
The two solutions are not equal in value, so, we can conclude that the system of equations has no solution, or is inconsistent.
hope this helps!
How much would a 20% tip be on a $65 restaurant bill?
Answer:
13 dollars would be the answer you're welcome lol
When p = 12, t = 2, and s = one-sixth, r = 18. if r varies directly with p and inversely with the product of s and t, what is the constant of variation? one-eighth one-half four and one-half 18
The constant of variation given that r varies directly with p and inversely with the product of s and t is one-half
From the question given above,r ∝ p ∝ 1/st
r ∝ p / st
r = Kp / st
Cross multiply
r × st = Kp
Divide both side by p
K = rst / p => constant of variation
How to determine the constant of variation p = 12t = 2 s = one-sixth = 1/6r = 18Constant of variation (K) =?K = rst / p
K = (18 × 1/6 × 2) / 12
K = 6 / 12
K = 1 / 2 = one-half
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Can someone please give me the (Answers) to this? ... please ...
I need help….
Answer:
see explanation
Step-by-step explanation:
2 chords intersecting inside a circle , then the product of the parts of one chord is equal to the product of the parts of the other chord.
6
BE × ED = AE × CE , that is
10 × 3x = 12(2x + 1) ← distribute parenthesis by 12
30x = 24x + 12 ( subtract 24x from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
then
ED = 3X = 3(2) = 6
7
RJ × JP = SJ × JQ , that is
6 × 3x = 4(4x + 1) ← distribute parenthesis by 4
18x = 16x + 4 ( subtract 16x from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
then
RP = RJ + JP = 6 + 3x = 6 + 3(2) = 6 + 6 = 12
Let x = 0.147 and let y = 0.147
The value of y will be more as the number is repetitive, and both x and y initial three digits after the decimal are the same.
What is a rational number?A rational number is one that has the form p/q, where p and q are integers and q is greater than zero. Some rational number examples are 1/3, 2/4, 1/5, 9/3, and so on.
The complete question is, Let x = 0.147 and let y = [tex]0.\overline{147}[/tex]. Is x a rational number? Is ya rational number? Which is larger, x or y?
Given the value of x is 0.147. As it can be written in the form of a fraction,
[tex]0.147 = \dfrac{147}{1000}[/tex], we can conclude that x is a rational number.
The value of y = [tex]0.\overline{147}[/tex] can also be written in the form of a fraction,
[tex]0.\overline{147} = \dfrac{147}{999}[/tex], therefore, we can conclude that y is also a rational number.
The value of y will be more as the number is repetitive, and both x and y initial three digits after the decimal are the same.
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The first thing you should do in solving a word problem is estimate what you think the answer would be.
True
False
Answer:
The answer is True.
Step-by-step explanation:
Estimate the Answer Before Solving Having a general idea of a ballpark answer .Or the problem lets students know if their actual answer is reasonable or not.help me i need help.
Answer:
The value of a side = 5
Step-by-step explanation:
By using PGT theoram
H² = P² + B²
=> 13² = a² + 12²
=> 13² - 12² = a²
=> 169 -144 = a²
=> 25 = a²
=> √25 = a
=> 5 = a
Answer:
a = 5
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
a² + 12² = 13²
a² + 144 = 169 ( subtract 144 from both sides )
a² = 25 ( take square root of both sides )
a = [tex]\sqrt{25}[/tex] = 5
A cylinder with radius 3 feet and height 5 feet is shown.
6
ft
Enter the volume, in cubic feet, of the cylinder. Round your
answer to the nearest hundredth.
Answer:
The volume of the cylinder is 141.23 cubic feet
Step by step explanation :
Given-
Radius of cylinder = 3 feet Height of cylinder = 5 feetNow, we know that
[tex] \boxed {\mathfrak \red{ volume \: of \: cylinder = \pi {r}^{2} h}}[/tex]where, r is the radius of the cylinder & h is the height of the cylinder.
Now,
Volume of the cylinder = [tex] \frac{22}{7} \times {3}^{2} \times 5[/tex]
[tex] = \frac{22}{7} \times 3 \times 3 \times 5[/tex]
[tex] = \frac{990}{7} [/tex][tex] = 141.428571[/tex] ( approximately )
[tex] = \boxed{ 141.43 \: \mathfrak { {ft}^{3}} }[/tex]
Which graph represents the function
f(x) = (x + 4)(x + 1)(x - 3)
?
Answer:
Step-by-step explanation:
The graph that represents the function
f(x) = (x + 4)(x + 1)(x - 3)
crosses the x-axis three times: at x = -4, x = -1, and x = 3
because we apply the zero product rule and found the roots -4, -1, and 3
x+ 4= 0 → x = -4
x+1 = 0 → x = -1
x-3 = 0 → x = 3
A rectangular table top has length 1. 7 m and width 0. 9 m. A force of 750 N is applied to the whole table top. Calculate the pressure in N/m2 to the nearest integer
Step-by-step explanation:
pressure = F/A
= 750/ (1.7×9)
= 49 N/m²
Please help i need answer asap
Answer:
14x+6+(5x+30+=2190
Step-by-step explanation:
Parallelogram Properties - Diagonals
delta math
Answer:
DE=18
Step-by-step explanation:
The reason is because that parallelogram ABCD has most of the sides equal to each other.
The length of DB = 36 and half of 36/2 gets us DE.
DE=36/2=18
DE=18 also equals to BE=18
Diagonals of a parallelogram bisect each other
So
DE+BE=DBPutting DE=BE
2DE=DBDE=DB/2DE=36/2DE=18Graph f(x) = 4[x] +5.
a.
b.
X
C.
d.
r
16
Answer:
C
Step-by-step explanation: