answer:
N(t)=2×[tex]1.7^{t}[/tex]
17
15
step by step explain:
before lesson (t=0), she knows 2 words.
after a week (t=1), she knows
2×(1+70%)=3.4 words
after one more week (t=2), she knows
3.4×(1+70%)=5.78 words
one more week later (t=3), she knows
5.78×(1+70%)=9.826 words
and so on ...
from pattern shown above, we know that she knows
2×[tex]1.7^{t}[/tex] words after t weeks
so N(t)=2×[tex]1.7^{t}[/tex]
after 4 weeks (t=4), she knows 2×[tex]1.7^{4}[/tex]=16.7042≈17 words
for learning 5000 words, she need:
2×[tex]1.7^{t}[/tex]=5000
[tex]1.7^{t}[/tex]=2500
t log(1.7)=log(2500)
t=[tex]\frac{log(2500)}{log(1.7)}[/tex]
=14.7448727
≈15 (round up)
Answer:
(a) N(t) = 2(1.7)^t
(b) 17
(c) 15
Step-by-step explanation:
(a) N(t) = 2(1.7)^t
There is a 2 because she starts with 2 words. The 1.7 is since her vocabulary grows by 70%. Finally, t represents the weeks. (it is an exponent)
(b) Just plug in the equation
N(4) = 2(1.7)^4
N(4) = 2(8.3521)
N(4) = 16.7042
Round, so it is 17
(c) Once again, plug in the equation
5000 = 2(1.7)^t
2500 = (1.7)^t
use a calculator for the part below
log1.7(2500) = log1.7(1.7)*t
t = log1.7(2500)
t = 14.7448
Round, so it is 15
What is the slope of the line
Answer:
Slope = 3
Step-by-step explanation:
Take two points and find the slope:
[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{3-0}{-1-(-2)}\\\\m=\frac{3}{1}=3[/tex]
Runner A runs at 10 km/h due north. Runner B leaves the same spot and runs at 12 km/h due east. Find the distance and bearing of runner B from runner A after 30 minutes
Answer: [tex]7.81\ km[/tex]
Step-by-step explanation:
Given
Runner A runs towards North at speed of 10 km/h
Runner B runs towards East at speed of 12 km/h
After half hour, they covered a distance of
[tex]\Rightarrow d_a=10\times 0.5\\\Rightarrow d_a=5\ km[/tex]
[tex]\Rightarrow d_b=12\times 0.5\\\Rightarrow d_b=6\ km[/tex]
They are running in perpendicular direction to each other
So, the distance between them is given by
[tex]\Rightarrow d=\sqrt{d_a^2+d_b^2}\\\Rightarrow d=\sqrt{5^2+6^2}\\\Rightarrow d=\sqrt{61}\\\Rightarrow d=7.81\ km[/tex]
Please help me.....................
Answer:16500
Step-by-step explanation:
That is, for every 100 people, there are 26 people aged between 11 and 20. So 63500 will have 16500 people aged 20.
PLZ HELP ANY GUESS WOULD HELP
Answer:
1st onne I believe I couldd be wrong but thats what I got
Step-by-step explanation:
What is the constant of proportionality in the equation y=\dfrac{5}{9}xy= 9 5 xy, equals, start fraction, 5, divided by, 9, end fraction, x? constant of proportionality ==equals
Answer:
5/9
Step-by-step explanation:
If a variable y is directly proportional to x, then;
y = kx where;
k is the constant of proportionality
Given the expression y = 5/9 x
On comparing with the general formula;
kx = 5/9 x
k = 5/9
Hence the constant of proportionality of the expression is 5/9
Answer:
5/9
Step-by-step explanation:
i tried it on khan and its right trust me
Find the circumference for the circle. use 3.14 for pi
A. 25.12 m.
B. 12.56 m.
C. 7.14 m.
D. 50.24 m.
Answer: 50.24
Step-by-step explanation:
=3.14x4 squared
=3.14x16
=50.24
The figure below is a square. Find the length of side x in simplest radical form with a
rational denominator.
VT
Answer:
x = [tex]\sqrt{14}[/tex]
Step-by-step explanation:
[tex]\sqrt{7}[/tex] / sin(45) = x / sin(90) (Cause its a square, the edges are 90 degrees)
[tex]\sqrt{14}[/tex] = x / 1
x = [tex]\sqrt{14}[/tex]
find the base of the triangle when the area is 94.5
Answer:
Base = 10.5 cm
Step-by-step explanation:
GIVEN :-
Height of the triangle = 18 cmArea of the triangle = 94.5 cm²TO FIND :-
The base of the triangleGENRAL FORMULAE TO BE USED IN THIS QUESTION :-
For a triangle with height 'h' & base 'b' , its area = [tex]\frac{1}{2} \times b \times h[/tex]
SOLUTION :-
[tex]Area = \frac{1}{2} \times Base \times Height[/tex]
[tex]=> 94.5 = \frac{18b}{2}[/tex]
Multiply both the sides by 2[tex]=> \frac{18b}{2} \times 2 = 94.5 \times 2[/tex]
[tex]=> 18b = 189[/tex]
[tex]=> b = \frac{189}{18} = 10.5[/tex]
Can someone help me solve this Algebraic Equation please?
x^1/2 + 3x^-1/2 = 10x^-3/2
Answer:
x=2
Step-by-step explanation:
Find Sin/Cos/Tan and Csc/Sec/Cot of A.
Answer:
Sin A = 5/13,
Cos A = 12/13,
tan A = 5/12
CSC A = 13/5
Sec A = 13/12
Cot A = 12/5
Lines J and k intersect at point Q and h is a straight line. What is the value of X ?
Answer:
Step-by-step explanation:
Angles on a straight line add up to 180 so 180-135 equals 45. Vertically opposite angles are equal so the second angle inside the triangle equals 100. Henceforth, we can solve this equation:
x +45+100 = 180 (angles in triangle add up to 180)
x+145=180
x=35
Vertically opposite angles are equal so x will become 35.
Hope this helps!
Helpppppp me please
Answer:
x=2
Step-by-step explanation:
The x is known which means that it is the one that is parallel to the y axis.
Answer:
x = 2
Step-by-step explanation:
The y axis is a vertical line
x = 2 would create a vertical line making it parallel with the y axis
Please help me this is due very soon!(Q13)
Answer:
Step-by-step explanation:
9) (25-x^2 )(a+2) = (5-x)(5+x)(a+2)
11) 9(v-3)+u^2(3-v)
9(v-3)+u^2( -v+3)
9(v-3)-u^2( v-3)
(9-u^2)(v-3)
(3-u)(3+u)(v-3)
can you guys help me fill the right angle measures
Answer:
3 = 20
5 = 20
8= 160
Step-by-step explanation:
angle 2 and 3 are on the same line, so 180 - 160 is 20 degrees
rule of alternate interior angles: angle 5 is equal to 3
rule of alternate exterior angles: angle 8 is equal to 2
given the similar triangles at the left, identify the scale factor.
PLEASE HELPPPPPPPPPPPP
Un frutero ha comprado 165kg de manzanas a 2 € el kilo; se le han estropeado 15 kg y el resto los vende a 4 € el kilo. ¿ Cuánto ha ganado? ( 1,25p)
Answer:
€270
Step-by-step explanation:
If a fruit vendor has bought 165kg of apples at € 2 per kilo, the total amount spent is expressed as;
Cost price = 165 * 2 = €330
If 15kg spoilt, the amount of fruit remaining will be 165 - 15 = 150kg
If he rests he sells for € 4 per kilo, then;
Selling price = 150 * 4 = €600
Amount earned = €600 - €330
Amount earned = €270
what is the zero of the function
Answer:
A
Step-by-step explanation:
The zero is the value of x where the line crosses the x- axis
The line crosses the x- axis at x = - 5 ← zero
Answer:
-5
Step-by-step explanation:
The zero of a function is the x-value of the location where the function intersects the x-axis.
Here I read at (-5,0), the function intersects the x-axis, so the zero of the functiion is x = -5
work out the average speed of 40 km in 2.5 hours
Answer:
19.20
Step-by-step explanation: used
a calc
CAN SOMEONE HELP ME ASAP????
Find the gradient of the line 2y = -10x + 1
Answer:
Gradient = -5
Step-by-step explanation:
The gradient of a line is the slope of the line.
The standard form of the line equation is y = mx + b
where m is the slope ( or gradient) b is the y - intercept.
Given :
2y = -10x + 1
[tex]y = -\frac{10}{2} x + \frac{1}{2}\\\\y = -5x + \frac{1}{2}\\\\Therefore , \ gradient \ is \ -5[/tex]
The gradient of the line whose equation is 2y=-10x+1 is -5.
What is gradient?Gradient could be a measure of how steep a slope or a line is.
How to calculate the gradient of the line?The equation of the road is 2y=-10x+1
y=-5x+1/2
Therefore the gradient of the line is that the coefficient of x which is -5.
Hence the gradient of the line is -5.
Learn more about gradient at https://brainly.com/question/23016580
#SPJ2
Solve for x. Enter the solutions from least to greatest. Round to two decimal places. (x+7)^2 - 11 = 0
Answer:
lesser x = -10.32
greater x = -3.68
Step-by-step explanation:
PLEASE HELP ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPp
Answer:
M1=44 M2=136 M3=44 M4=136
Step-by-step explanation:
M3= 44 so M1=44 due to opposite angles being equal
then if two of the angles add to 88
360-88= 272
divide 272 by 2 as M2 and M4 are equal
272/2=136
Answer:
m∠1 = 44°
m∠2 = 136°
m∠4 = 136°
Step-by-step explanation:
m∠1 explanation:
I got it from m∠3 since they're both congruent
m∠2 explanation:
Since we already have the measure of 3 and 1, we can easily add both of the measures (44 + 44 = 88°) then subtract it from 360° (total) = 272°
Then since both measures (2 and 4) are congruent (measuring the exact same length and angle) we can divide 272° ÷ 2 = 136°
m∠4 explanation:
I got it from m∠2 since they're both congruent
Find the missing side
Answer:
x = 71.5 in
Step-by-step explanation:
Remember the SOHCAHTOA rule
Soh...
Sine = Opposite / Hypotenuse
...cah...
Cosine = Adjacent / Hypotenuse
...toa
Tangent = Opposite / Adjacent
In this case, we use: CAH.
cos(52) = 44/x
x = 44/cos(52)
x = 71.5 inches
Left parenthesis 5 plus 2 square root of 6 right parenthesis squared = a plus b square root of 6 then the value of a and b are
Answer:
The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.
Step-by-step explanation:
The statement is equivalent to the following mathematic expression:
[tex]\left(5 + 2\sqrt{2})^{2} = a + b\cdot \sqrt{6}[/tex] (1)
By definition of the perfect square trinomial:
[tex]25 + 20\cdot \sqrt{2} + 8 = a + b\cdot \sqrt{6}[/tex]
[tex]33 + 20\sqrt{2} = a + b\cdot \sqrt{6}[/tex]
And by direct comparison we have the following system:
[tex]a = 33[/tex] (2)
[tex]b\cdot \sqrt{6} = 20\sqrt{2}[/tex] (3)
By (3), we solve for [tex]b[/tex]:
[tex]b = \frac{20}{\sqrt{3}}[/tex]
[tex]b = \frac{20\sqrt{3}}{3}[/tex]
The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.
Use technology to find the line of best fit for the following data.
(1, 0), (2, 3), (3,1), (4,4), (5,5)
When the equation of the line is in the form y=mx+b, what is the value of **b**?
Enter your answer as a decimal rounded to the nearest tenths place, like this: 42.5
Given:
The data points are:
(1, 0), (2, 3), (3,1), (4,4), (5,5)
To find:
The equation of best fit line in the form of [tex]y=mx+b[/tex] and then find the value of b.
Solution:
The general form of best fit line is:
[tex]y=mx+b[/tex] ...(i)
Where, m is the slope of best fit line and b is the y-intercept of the line.
Using the graphing calculator, we get the equation for the best fit line and the equation is
[tex]y=1.1x-0.7[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]b=-0.7[/tex]
Therefore, the value of b is equal to -0.7.
What is the value of x in the triangle?
Round your final answer to the
nearest hundredth
Given:
In a right angle triangle,
Hypotenuse = 25 cm
Base = x
Angle between base and hypotenuse = 18 degrees.
To find:
The value of x.
Solution:
In a right angle triangle,
[tex]\cos \theta =\dfrac{Base}{Hypotenuse}[/tex]
In the given right triangle,
[tex]\cos (18^\circ) =\dfrac{x}{25}[/tex]
[tex]\cos (18^\circ) \times 25=x[/tex]
[tex]0.9510565 \times 25=x[/tex]
[tex]23.7764125=x[/tex]
Round the answer to the nearest hundredth (two decimal).
[tex]x=23.78[/tex]
Therefore, the value of x is about 23.78 cm.
You want to estimate the number of students in your school who support extra funding for the history club. You survey every ninth student who enters the
school.
Determine whether the sample is based or unbiased
Answer:
unbiased
Step-by-step explanation:
it would be biased if you lets say survey the history club kids
what is the answer? can someone help
Answer: Choice B
Explanation: The rule you use is [tex]\sqrt{m*n} = \sqrt{m}*\sqrt{n}[/tex]
Answer:
Step-by-step explanation:
A: is not the answer. The answer is √144 which is 12
B: is correct. You can do it this way, by breaking the 9 and 16 apart.
C: I don't know exactly what the logic of 36 is, but it is not the right answer.
D: I can't explain why the choice would be division. It is multiplication of some sort. D is incorrect.
ASAP brainliest if right
How does the graph of f(x) = |x| compare with the graph of g(x) = −2|x|? Select all that apply.
A. The graph of g is a vertical compression of the graph of f.
B. The graph of g is a vertical stretch of the graph of f.
C. The graph of g is a reflection over the x-axis of the graph of f.
Answer:
option A
Step-by-step explanation:
y = k . f( x )
• if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically stretched by multiplying each of its y-coordinates by k.
• if 0 < k < 1 (a fraction), the graph is f (x) vertically shrunk (or compressed) by multiplying each of its y-coordinates by k.
• if k < 0, the vertical stretch or shrink is followed by a reflection across the x-axis.
Given g(x ) = - |x |
= -1 × f(x)
k < 0 , therefore the graph g (x) is a vertical shrink ( or compression ) of graph f
If f(x) = 2x²+2 and g(x) = x² - 1 ,find (f- g)(x).
A. 3x² +3
B. 3x² +1
C. x² +1
D. x² +3
Step-by-step explanation:
(F-g) (X)
= f(x) - g(x)
(2x² + 2 )-(x²-1) =
3x²+3
Determine whether the triangles are congruent. Explain your reasoning .
SAS (Side, Angle, Side) or ASA (Angle, Side, Angle)
Answer:
Step-by-step explanation:
The two triangle are congruent for the rule SAS
QP congruent to TU
angle P and angle T are both right
side PR is in common