Answer:
Step-by-step explanation:
s^2 represents the area of a square whose side length is s.
(8x)^2 represents the area of a square whose side length is 8x.
9. A bank pays interest of 11% on $6000 in a deposit account
After how many years will the money have trebled?
Answer:
Approximately 6.642 years
Step-by-step explanation:
The given parameters are;
The amount in the deposit account = $6,000
The time in which the money will have trebled at 11% compound interest, is given as follows;
[tex]A = P\times \left (1 + \dfrac{r}{n} \right )^{n\cdot t}[/tex]
Where;
A = The amount at the end of the period
P = The amount in the deposit = $6,000.00
r = The rate of interest = 11%
t = The periods that elapsed
n = The number of times the interest is applied per period of time, t = 1
For the money to have trebled, the amount generated at the end of the period will be 200% the amount deposited
Therefore, we have;
Amount, A, at the end of period = 200/100× $6,000 = $12,000
Substituting the values into the formula for the formula, we have;
[tex]\$ 12,000 = \$ 6,000\times \left (1 + \dfrac{0.11}{1} \right )^{1\times t}[/tex]
Which gives;
[tex]\$ 12,000 = \$ 6,000\times \left (1 + {0.11} \right )^{t}[/tex]
[tex]\left (1 .11} \right )^{t} = \dfrac{ \$ 12,000}{\$ 6,000} = 2[/tex]
t = ㏒(2)/(㏒(1.11)) ≈ 6.642 years which is approximately 6 years, 7 months and 24 days
Which undefined terms are needed to define a line segment?
Answer: The correct answer is point and line. Explanation: These are two of the fundamental undefined terms in geometry. A line segment is a part of a line that has two defined points at each end; therefore "line" and "point" are used in the definition.
Step-by-step explanation:
The undefined terms which are needed to define a line segment are Point and line.
Line Segment: A line segment is a part of the line that connects two endpoints. A line is also the shortest distance between the two points.Undefined terms: Point: A Point indicates a location that has no size. Line: A line is a set of continuous points, which extends continuously at both ends.
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Given r(3,7,-1), S(10,-4,0) find an ordered triple that represents RS and find the magnitude of RS. a.(5,-11,3), 3sqrt19 b.(7,-11,1), 3sqrt19 c.(5,-11,3), 7sqrt15 d.(7,-11,1), 7sqrt15
Answer:
[tex]|RS| = \sqrt[3]{19}[/tex]
Step-by-step explanation:
The computation of the magnitude is shown below:
Data provided in the question
Given points
R(3,7,-1), S(10,-4,0)
Now the distance lies between R and S
RS = (10 ,-4, 0) - ( 3 ,7, -1 )
= (10 - 3, -4 - 7, 0 - (- 1))
= (7, - 11, 1 )
After that, the magnitude is determined by using the following calculation part
[tex]|RS| = \sqrt{(7)^2 + (-11)^2 + (1)^2} \\\\ = \sqrt{49 + 121 + 1} \\\\ = \sqrt{121}\\\\ = \sqrt[3]{19}[/tex]
19x+rx= -37x+w what is the x
Answer:
x = w / (56 + r)
Step-by-step explanation:
Given the equation :
19x + rx= -37x + w ; find x
Collecting like terms
19x + rx + 37x = w
Factorizing x in the Left hand side
x(19 + 37 + r) = w
x(56 + r) = w
Therefore we can obtain x by dividing both sides by (56 + r)
x(56 + r) / (56 + r) = w / (56 + r)
x = w / (56 + r)
Se cocina una pizza de 20 cm de radio, en su interior se coloca al azar 12 piezas de salami
circular de 1 cm de radio y en al área restante se pondrá queso.
¿Qué área se tiene para el queso? (Expresar el resultado en términos de 7)
Answer:
The area of cheese is 388π cm.
Step-by-step explanation:
Given that,
Radius of pizza = 20 cm
Number of pieces = 12
Radius of circle = 1 cm
We need to calculate the area of pizza
Using formula of area
[tex]A=\pi\times r^2[/tex]
Put the value into the formula
[tex]A=\pi\times20^2[/tex]
[tex]A=400\pi\ cm^2[/tex]
We need to calculate the area of circle
Using formula of area
[tex]A'=\pi\times r^2[/tex]
Put the value into the formula
[tex]A'=\pi\times1^2[/tex]
[tex]A'=\pi\ cm^2[/tex]
Now, we multiply the result by 12 because they are 12 salamis.
So. the area of salamis will be
[tex]A'=12\pi\ cm^2[/tex]
We need to calculate the area of cheese
The total area of the pizza and subtract the area of the salamis
[tex]A''=A-A'[/tex]
Put the value in to the formula
[tex]A''=400\pi-12\pi[/tex]
[tex]A=388\pi\ cm^2[/tex]
Hence, The area of cheese is 388π cm.
describe a situation that could be modeled with the ration 4:1
Answer:
There could be many situations that use this ratio, but one example could be For every 4 pencils purchased 1 large eraser will be purchased.
But, as said before anything can be used as an example.
A retailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which represents the situation, where x is the original cost of the item(s)?
Answer:
C
Step-by-step explanation:
C on edge
Considering the discount and the sales tax, the equation that represents the situation is:
[tex]C(x) = 0.6955x[/tex]
-------------------------------
The original price, without discount, is of x.Promotional sale for 35% off all items, which means that the amount paid is 100% - 35% = 65% of the original price, thus x is multiplied by 0.65.7% sales tax means that x is also multiplied by 100% + 7% = 107% = 1.07.Thus, the equation that represents the cost is:
[tex]C(x) = x \times 0.65 \times 1.07 = 0.6955x[/tex]
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Suppose the test scores of students in a class are normally distributed with a mean of 86 and a standard deviation of 4. What is the z-score for a student that scored 76 on a test? A.−4 .−2.5 C.2.5 D.4
Answer:
-2.5
Step-by-step explanation:
Here in this question, we are interested in calculating the z-score for a student that had a particular mark at the test
To calculate the z-score, we need to use a mathematical formula
Mathematically;
z-score = (x - mean)/SD
From the question;
x = 76
mean = 86
standard deviation SD = 4
Plugging these values in the equation, we have;
z-score = (76-86)/4 = -10/4 = -2.5
There are a total of 84 people, lions, and giraffes at the zoo. Cassie visits the
zoo and counts 282 total legs. If you were to double the number of people,
that is equivalent to tripling the number of lions. How many of each are at the
zoo?
Answer:
14 giraffes, 28 people and 42 lions
Step-by-step explanation:
you add how many legs for all 3 x1
add this you have a total 14
double that is 28 triple that is 42
total 84
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
mBC ≈ 20.5
Step-by-step explanation:
Law of Sines: [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
Simply plug in it into the formula.
Step 1: Define variables
c = 16
C = 52°
A = 84°
BC = x
Step 2: Plug into formula
[tex]\frac{16}{sin51} =\frac{x}{sin84}[/tex]
Step 3: Solve
[tex]sin84(\frac{16}{sin51}) = x[/tex]
x = 20.4754
x ≈ 20.5
How many dots are there at t minutes? Solve the problems by your preferred method. Your
solution should indicate how many dots will be in the pattern at 3 minutes, 100 minutes,
and t minutes. Be sure to show how your solution relates to the picture and how you
arrived at your solution.
The image to the question is missing, but I found a matching image, which is attached to this solution
Answer:
3 minutes = 13 dots
100 minutes = 401 dots
t minutes = 4(t) + 1 dots
Step-by-step explanation:
From the image, the following can be noticed:
time (Mins) dots
0 1
1 5
2 9
The pattern gotten from this progression is that, if the time is multiplied by 4, and the result added to one, the result will be the number of dots.
hence, when the time is 0 minutes:
0 × 4 = 0
0 + 1 = 1 ( 1 dot)
when the time is 1 minute
1 × 4 = 4
4 + 1 = 5 (5 dots)
when the time is 2 minutes
2 × 4 = 8
8 + 1 = 9 ( 9 dots)
Therefore,
when the time = 3 minutes
3 × 4 = 12
12 + 1 = 13 dots
at 100 minutes:
100 × 4 = 400
400 + 1 = 401 dots
at t miutes
t × 4 = 4t
4t + 1 = number of dots
Therefore number of dots at t minutes = 4(t) + 1
Jacques is standing 1200 meters from a
cliff he is planning to climb. The angle of
elevation from the ground to the top of the
cliff is 35º. To the nearest meter, how tall is
the cliff?
Answer:568.58
Step-by-step explanation:
Tan(35)=h/1200
1200tan(35)=h
568.57766=h
568.58
A company offered 200 cameras at a 15% discount during a 5-day sale
The bar graph shows the number of cameras sold at the end of each day.
Day 1 - 30
Day 2 - 40
Day 3 - 50
Day 4 - 25
Day 5 - 40
(a) Find the percentage increase in the number of cameras sold on Day 5 as compared to Day 4.
Answer:
60%
Step-by-step explanation:
Cameras sold on Day 4 = 25, on Day 5 = 40
The difference in numbers of sold cameras = 40 - 25 = 15
The increase is 15 cameras.
Percentage increase:
15/25*100% = 60%Answer is 60% increase on Day 5 compared to Day 4
f(x)= (1,2) (3, -4) (-5, -8)
Answer: y= 156
Step-by-step explanation:
y= 12(3-4) (-5 -8)
2 which of the following is a perfect cube
a) 400 -
D. 3375–
C 8000 -
Answer:
8000 is a perfect cube but 3375 can be also but i m a little sure that 8000 is a perfect cube
When drawing the arcs in order to bisect a line segment, why must the width of the compass be more than half of the length of
the segment? (1 point)
of the compass is not opened that wide, the arcs will not intersect, making the subsequent steps impossible
This is simply a loose guideline and the actual width of the compass does not matter
If the compass is opened wider than that, for example just less than the full length of the line segment, the arcs will not intersect
making the subsequent steps ingyssible
Bisecting means to divide something evenly in half, so the compass should be a little bit wider than half the length of the line segment
but not wider than three-fourths of the length of line segment
Answer: Choice A
If the compass isn't open wide enough, then the arcs won't intersect forming the points we need to create the perpendicular bisector.
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Answer:
a
Step-by-step explanation:
Why is f(x)=(3x+13)2+89 not the vertex form of f(x)=9x2+2x+1?
Answer:
Step-by-step explanation:
Given function in the vertex form is,
f(x) = (3x + 13)² + 89
= [tex]9(x+\frac{13}{3})^{2}+89[/tex] --------(1)
Vertex of the parabola → [tex](-\frac{13}{3},89)[/tex]
If the standard equation of this function is,
f(x) = 9x² + 2x + 1
We will convert it into the vertex form,
f(x) = 9x² + 2x + 1
= [tex]9(x^{2}+\frac{2}{9}x)+1[/tex]
= [tex]9[x^{2}+2(\frac{1}{9})x+(\frac{1}{9})^{2}-(\frac{1}{9})^2]+1[/tex]
= [tex]9[x^{2}+2(\frac{1}{9})x+(\frac{1}{9})^{2}]-9(\frac{1}{9})^2+1[/tex]
= [tex]9[x^{2}+2(\frac{1}{9})x+(\frac{1}{9})^{2}]-(\frac{1}{9})+1[/tex]
= [tex]9(x+\frac{1}{9})^2+\frac{9-1}{9}[/tex]
= [tex]9(x+\frac{1}{9})^2+\frac{8}{9}[/tex] -------(2)
Vertex of the function → [tex](-\frac{1}{9},\frac{8}{9})[/tex]
Equation (1) and (2) are different and both the equations have different vertex.
Therefore, given equation doesn't match the equation given in the vertex form of the function.
The theoretical probability of a customer
walking into Andy's deli and purchasing a
sandwich is 6 in 10. Which of the
following predictions about Andy's deli is
most likely true?
If y varies inversely as x, and y = 6 when x = 24, find x when y = 18
Answer:
x = 8
Step-by-step explanation:
Standard form for inverse variation:
y = k/x
We now use the given information to find k.
y = 6 when x = 24
6 = k/24
k = 6 * 24
k = 144
The equation for this inverse relation is
y = 144/x
For y = 18, we get
18 = 144/x
18x = 144
x = 144/18
x = 8
Answer:
x = 8Step-by-step explanation:
To find the value of x when y = 18 we must first find the relationship between them.
The statement
y varies inversely as x is written as
[tex]y \: \: \alpha \: \: \frac{k}{x} [/tex]where k is the constant of proportionality
From the question when
y = 6
x = 24
Substitute the values into the above equation
That's
[tex]6 = \frac{k}{24} [/tex]Cross multiply
That's
k = 24(6)
k = 144
So the formula for the variation is
[tex]y = \frac{144}{x} [/tex]When
y = 18
[tex]18 = \frac{144}{x} [/tex]Cross multiply
18x = 144
Divide both sides by 18
x = 8Hope this helps you
solve for n: 4^n×2^-18=1
One way to do it is by cleverly rewriting terms and using some basic algebraic identities:
[tex]4^n\cdot 2^{-18}=1[/tex].
[tex]2^{2n-18}=2^0[/tex].
[tex]2n-18=0[/tex].
[tex]n=18/2=\boxed{9}[/tex].
Another way would be to use logarithms, namely:
[tex]4^n\cdot2^{-18}=1\implies n=\log_4\Big({\frac{1}{2^{-18}}}\Big)=\boxed{9}[/tex].
Hope this helps.
Answer:
n = 9.
Step-by-step explanation:
4^n = 1 / 2^-18
4^n = 2^18
2^2n = 2^18
2n = 18
n = 9.
Approximate the square root of 228 to the nearest hundredth.
Answer:
15.1
Step-by-step explanation:
15.1 times 15.1 = 228.01
Answer:
Nearest hundredth of 228 is 200 so the square root of 200 is 10under root 2.
Step-by-step explanation:
Hope it will help you :)
I do not know how to draw this in full scale
Answer:
use the actual dimensions on your drawing
Step-by-step explanation:
"Full scale" simply means you use the actual object dimensions on your drawing of it.
If you don't know the meaning of "plan view", "front elevation", or "side elevation," you may need to consult your curriculum materials or any of numerous references on mechanical drawing.
For this object, I would say a "front elevation" is the view from the point marked "Y". A "side elevation" is the view from the point marked "X". A plan view is the view from above.
__
If you draw, on paper, patterns for cutting out the pieces that make up the object, you will be well on your way to making the required drawings. For example, the face ABCPEF would represent the front elevation. (The only thing added on the drawing of it is a dashed line representing hidden line RQ 1 cm below line AB.)
The side elevation is the shape of AQHGF on top of the shape EMLD. On your drawing of it, the line for EM is the same line as the line representing FG.
The top (plan) view is the shape CPNK with lines in the appropriate places to represent the edges EM, FG, and RQ.
__
Orthogonal views of an object like this are different from the kind of drawing you would make if you were trying to make a "net" for folding or calculating surface area. A net has every face actual size. Here, every face is represented the way it would be seen from a given direction. Slanted faces never show up actual size.
Find the equation of the line in slope-intercept form that passes through the given points (-3,6) and (-1,3).
Answer:
[tex]\large\boxed{y=-\frac{3}{2}x+\frac{3}{2}}[/tex]
Step-by-step explanation:
Use the two-points slope equation: [tex]\boxed{m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]
Given the two coordinate points of [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex], implement these values into the equation and solve for m.
[tex]m=\frac{(3)-(6)}{(-1)-(-3)}\\\\m=\frac{(-3)}{(2)}\\\\m=-\frac{3}{2}[/tex]
The slope is then placed in the equation - y = -3/2x + b.
Then, insert a value for y and x from the same coordinate point to solve for b.
[tex]6=-\frac{3}{2}(-3)+b\\\\6=\frac{9}{2}+b\\\\\frac{3}{2}=b[/tex]
Then, plug it all in to get [tex]\large\boxed{y=-\frac{3}{2}x+\frac{3}{2}}[/tex].
Answer:
y=-3/2x
Step-by-step explanation:
First, find the slope with y2-y1/x2-x1=m
3-6 m=-3/2
--------- =
-1-+-3
Now plug it in to point slope form
Point slope form is y-y1=m(x-x1)
y-3=-3/2(x--1) Distribute -3/2 to x and 1
y-3=-3/2x-3 Add three on both sides to get y alone
y=-3/2x Three's cancel out. This is the final equation.
Simplify: 7 - 3(2x - 5) - 4x
Answer:
[tex]\Huge \boxed{2(-5x+11)}[/tex]
Step-by-step explanation:
[tex]7 - 3(2x - 5) - 4x[/tex]
Expanding brackets.
[tex]7-6x+15-4x[/tex]
Grouping like terms.
[tex](-6x-4x)+(7+15)[/tex]
Combining like terms.
[tex]-10x + 22[/tex]
Factoring the expression.
[tex]2(-5x+11)[/tex]
what is 3x + 4 = 12
Answer:
3x - 4 = 12
3x = 12 + 4
3x = 16 (divide both sides by 3 to get x)
3x/3 = 16/3
x = 5.333.......
Round the number below to the nearest tenth. x = 5.03126
Answer:
See Below:
Step-by-step explanation:
Tenths place is just 1 decimal place thus it is 5.0
Can someone help me with this its for biology but it’s a math question.
Answer:
Hey there!
A pie graph is best used for looking at the percentages in each category.
Let me know if this helps :)
Answer:
Pie charts are used to show percentage or proportional data.
10 = 7 - m*
It says solve & check solution. Can someone help asap
Answer:
see explanation
Step-by-step explanation:
Given
10 = 7 - m ( subtract 3 from both sides )
3 = - m ( multiply both sides by - 1 )
- 3 = m , or
m = - 3
As a check
Substitute m = - 3 into the right side of the equation and if equal to the left side then it is the solution
7 - m = 7 - (- 3) = 7 + 3 = 10 = left side
Thus m = - 3 is the solution to the equation
A triangle has sides with lengths of 5x - 2, 4x - 4, 6x - 8. What is the perimeter of the triangle?
Answer:
(15x - 4) units
Step-by-step explanation:
5x-2 + 4x-4 + 6x - 8
15x - 14
Find the measure of b. A. 14 B. 16 C. 74 D. 76
Answer:
D. 76
Step-by-step explanation:
a = 90°
a + b + 14 = 180°
90 + b + 14 = 180°
b = 180 - (90 + 14 )
b = 76°
The measure of ∠ b is 76°.
What is Cyclic Quadrilateral?
A Cyclic Quadrilateral is defined as a quadrilateral that is contained by a circle is referred to as a cyclic quadrilateral. This indicates that a circle connects the quadrilateral's four vertices. Concyclic vertices are referred to as such. Circumcenter and circumradius are terms used to describe the circle's center and radius, respectively.
According to given figure as:
Angle ∠ a = 90°
∠ a + ∠ b + 14° = 180° ( three angles of triangle)
90 + ∠ b + 14 = 180°
∠ b = 180 - 90 - 14
∠ b = 180 - 104
∠ b = 76°
Hence, the measure of ∠ b is 76°.
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