[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x^{-2}y^{-4}x^3)^{-2}\implies (x^{-2}x^3y^{-4})^{-2}\implies (x^{-2+3}y^{-4})^{-2}\implies (x^{1}y^{-4})^{-2} \\\\\\ \stackrel{\textit{distributing the exponent}~\hfill }{(x^{-2\cdot 1}y^{-2\cdot -4})\implies x^{-2}y^8}\implies \cfrac{1}{x^2}\cdot y^8\implies \cfrac{y^8}{x^2}[/tex]
Figure A is the preimage. Which figure is the image of figure A after a dilation with a scale factor of 3 and a center of (0, 0)?
A. Figure R
B. Figure S
C. Figure T
D. Figure U
The answer is option "D. Figure U"
Which equation can be used to solve the problem?
60 percent of what number is 30?
Answer:
50
Step-by-step explanation:
Let the unknown number be n. Then 0.60n = 30, and n = 30/0.60 = 50.
Answer:
60 divided by 2 =30
100 divided by 2 = 50 so your answer will be c
Step-by-step explanation:
hope your having a good day guys
A pet store owner set the price of a bag of cat food at 50% above the cost. When it did not sell, the price was reduced by 20%, to $12.00. What was the original cost?
Answer:
60
Step-by-step explanation:
Answer:
$10.
Step-by-step explanation:
Let x represent the original cost of bag of cat food.
We have been given that a pet store owner set the price of a bag of cat food at 50% above the cost. So the cost of cat food would be x plus 50% of x.
[tex]x+\frac{50}{100}*x\rightarrow x+0.5x=1.5x[/tex]
We are further told that the price was reduced by 20%, when it did not sell. So price of cat food after reduction would be [tex]1.5x[/tex] minus 20 percent of [tex]1.5x[/tex].
[tex]1.5x-(\frac{20}{100}\times 1.5x)[/tex]
[tex]1.5x-(0.20\times 1.5x)[/tex]
[tex]1.5x-(0.3x)[/tex]
[tex]1.2x[/tex]
Since price after reduction was $12, so we will equate [tex]1.2x[/tex] with 12 as:
[tex]1.2x=12[/tex]
[tex]\frac{1.2x}{1.2}=\frac{12}{1.2}[/tex]
[tex]x=10[/tex]
Therefore, the original cost of cat food was $10.
Which of the following could be the ratio between lengths of the two legs of a 30-60-90 triangle
Answer:
E and F.
Step-by-step explanation:
Let the side opposite the smallest angle have a measurement of x (this is the shortest side).
The hypotenuse is twice the shorter side so the hypotenuses would be 2x in this case.
The long leg is square root of 3 times the short side or sqrt(3)x in this case.
So the ratio of long leg to short leg is [tex]\frac{\sqrt{3}x}{x}=sqrt(3):1[/tex]
and
the ratio of short leg to long leg is [tex]\frac{x}{\sqrt{3}x}=1:sqrt(3)[/tex].
The answer is not A that division is equivalent to 1:1.
B same reason as A.
C is not right because 1:sqrt(2) is not the same as 1:sqrt(3)
I bolded the reason in C so you can see why I said that.
You can also put these in your calculator and compare the decimals like so:
D gives us 0.816 approximately while sqrt(3)/1 gives 1.73 and 1/sqrt(3) gives 0.58 approximately. 0.816 is neither one of those.
How about E? 1:sqrt(3) is exactly what one of our ratios say.
How about F? sqrt(3)/3=0.58 so this is what one of our ratios is equivalent to.
So E and F are your answers.
The only correct options are: E. [tex]\(1 : \sqrt{3}\)[/tex] and F. [tex]\(\sqrt{3} : 3\)[/tex].
To determine the correct ratios between the lengths of the legs of a [tex]\(30^\circ\)-\(60^\circ\)-\(90^\circ\)[/tex] triangle, we first recall the properties of such a triangle:
Step 1: In a [tex]\(30^\circ\)-\(60^\circ\)-\(90^\circ\)[/tex] triangle, the side lengths are in the ratio [tex]\(1:\sqrt{3}:2\)[/tex], where:
The shortest leg (opposite the [tex]\(30^\circ\)[/tex] angle) has length (1).
The longer leg (opposite the [tex]\(60^\circ\)[/tex] angle) has length [tex]\(\sqrt{3}\)[/tex].
The hypotenuse has length (2).
Step 2: Identify the correct ratio between the legs:
The ratio of the shortest leg to the longer leg is [tex]\(1:\sqrt{3}\)[/tex].
Now, let's analyze the given options:
A. [tex]\(\sqrt{2} : \sqrt{2}\)[/tex]: This ratio simplifies to (1:1), which is incorrect for a [tex]\(30^\circ\)-\(60^\circ\)-\(90^\circ\)[/tex] triangle.
B. [tex]\(\sqrt{3} : \sqrt{3}\)[/tex]: This ratio simplifies to (1:1), which is incorrect for a [tex](30^\circ\)-\(60^\circ\)-\(90^\circ\)[/tex] triangle.
C. [tex]\(1 : \sqrt{2}\)[/tex]: This does not match the ratio [tex]\(1 : \sqrt{3}\)[/tex].
D. [tex]\(\sqrt{2} : \sqrt{3}\)[/tex]: This does not match the ratio [tex]\(1 : \sqrt{3}\)[/tex].
E. [tex]\(1 : \sqrt{3}\)[/tex]: This matches the correct ratio [tex]\(1 : \sqrt{3}\)[/tex].
F. [tex]\(\sqrt{3} : 3\)[/tex]: This does not match the ratio [tex]\(1 : \sqrt{3}\)[/tex].
Thus, the only correct options are: E. [tex]\(1 : \sqrt{3}\)[/tex] and F. [tex]\(\sqrt{3} : 3\)[/tex]
Simplify h= 105sin (0.0698(90+1)) + 105
Answer:
[tex]h= 116.616[/tex]
Step-by-step explanation:
we have
[tex]h= 105sin (0.0698(90+1)) + 105[/tex]
step 1
Solve (90+1)
[tex]h= 105sin (0.0698(91)) + 105[/tex]
step 2
Solve 0.0698(91)
[tex]h= 105sin (6.3518) + 105[/tex]
step 3
Solve sin (6.3518)
[tex]h= 105(0.11063) + 105[/tex]
step 4
Solve 105(0.11063)
[tex]h= 11.616 + 105[/tex]
step 5
Solve 11.616 + 105
[tex]h= 116.616[/tex]
Simplify 3 sqrt 5x * 3 sqrt 25x^ 2 completely.
Answer: It’s D
5x
25x can still be simplified all the way down to 5x
(D) 5x Is the correct answer
why is 2 the only number that is always 4 when added multiplied or squared
Answer:
There are infinite numbers that added or multiplied will give the same answer. But, if the require this two numbers to be the same, then we need to solve the following equation to see what we found out:
x + y = x * y
Given that we want the numbers to be equal, then y=x.
x + x = x * x
2x = x^2
x^2 - 2x = 0
x(x-2) = 0
We find that NOT only x=2 meets this requirement but also x=0.
Therefore, there is another number that when added, multiplied or squared gives the same result. The other number is zero!
We can prove it:
0 × 0 = 0
0 + 0 = 0
The radius of the circle whose equation is (x - 3)² + (y + 1)² = 16 is
A). 4
B). 8
C). 16
The equation of a circle is written as (x-h)^2 + (y-k)^2 = r^2
Where the center point of the circle is (h,k) and r is the radius.
In the given equation 16 = r^2
To find r take the square root of both sides:
r = √16
r = 4
The answer is A.
Answer: OPTION A.
Step-by-step explanation:
The equation of a circle in center-radius form is:
[tex](x - h)^2 + (y- k)^2 = r^2[/tex]
Where the center is at the point (h,k) and "r" is the radius.
Then, given the equation of the circle:
[tex](x - 3)^2 + (y + 1)^2 = 16[/tex]
You can idenfity that:
[tex]r^2=16[/tex]
Therefore, in order to find the radius, you need to solve for "r".
Then, this is:
[tex]r=\sqrt{16}\\\\r=4[/tex]
What is a correct equation for the line passing through the point (-2,1) and having slope m=1/2
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We ahve the slope m = 1/2 and the point (-2, 1). Substitute:
[tex]y-1=\dfrac{1}{2}(x-(-2))[/tex]
[tex]y-1=\dfrac{1}{2}(x+2)[/tex] - point-slope form
Covert to the slope-intercept form (y = mx + b):
[tex]y-1=\dfrac{1}{2}(x+2)[/tex] use the distributive property
[tex]y-1=\dfrac{1}{2}x+1[/tex] add 1 to both sides
[tex]y=\dfrac{1}{2}x+2[/tex] - slope-intercept form
Convert to the standard form (Ax + By = C):
[tex]y=\dfrac{1}{2}x+2[/tex] multiply both sides by 2
[tex]2y=x+4[/tex] subtract x from both sides
[tex]-x+2y=4[/tex] change the signs
[tex]x-2y=-4[/tex] - standard form
Convert to the general form (Ax+By+C=0):
[tex]x-2y=-4[/tex] add 4 to both sides
[tex]x-2y+4=0[/tex] - general form
carlene has 104 pieces of candy left over from halloween. she would like to distribute them evenly to the 8 kids on her block. write an equation to show how many pieces of candy each kid will receive
Answer: Each kid would receive 13 pieces of candy
Step-by-step explanation: Since Carlene has 104 pieces of candy and she wants to distribute them evenly to 8 kids she would have to do division and divide 104 with 8 which equals to 13 which means 13 pieces of candy are going to each kid.
Answer: Our required equation would be
[tex]\dfrac{\text{Number of pieces of candy}}{\text{Number of kids}}[/tex]
and each kid would get 13 pieces of candy.
Step-by-step explanation:
Since we have given that
Number of pieces of candy left over from halloween = 104
Number of kids in which she would like to distribute = 8
As every student get pieces of candy evenly.
So, Number of pieces of candy each kid would get is given by
[tex]\dfrac{\text{Number of pieces of candy}}{\text{Number of kids}}\\\\=\dfrac{104}{8}\\\\=13[/tex]
Hence, our required equation would be
[tex]\dfrac{\text{Number of pieces of candy}}{\text{Number of kids}}[/tex]
and each kid would get 13 pieces of candy.
classify the following triangle. check. check all that apply
Step-by-step explanation:
the triangle is obtuse...has an angle greater than 90deg
also it is scalene...all 3 sides are different length
The triangle is a scalene and obtuse triangle
What is a Scalene Triangle?A scalene triangle is a type of triangle with three different length sides and three interior angles that add up to 180 degrees. Scalene triangles have no equal of parallel sides , hence there is no line of symmetry. The interior angles of a scalene triangle can be acute , right or obtuse angles.
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of sides of the triangle are
The measure of side AB = 11.9
The measure of side BC = 7
The measure of side AC = 6
And , the measure of ∠ABC = 132°
So , the sides of the triangle are having different lengths so it can be classified as a scalene triangle
And , the angle is obtuse , so it is also an obtuse triangle
Hence , the triangle is scalene
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Which line segment is drawn in the figure?
Answer:
C) XZ is your best answer.
Step-by-step explanation:
Note that all the other choices are not line segments:
YZ is an arc segment, and is not your answer.
WY is also an arc segment, and is not your answer.
WZ is not a straight line, which does not make it a "line segment" (a straight line that is terminated on both ends by points).
~
Answer: The answer is C
if you apply the changes below to the quadratic parent function, f(x)=x^2, what is the equation of the new function? shifted 1 unit right. vertically streched by a factor of 5. reflected over the x-axis.
Answer:
[tex]f(x) = - 5 {(x - 1)}^{2} [/tex]
Step-by-step explanation:
The given parent function is:
[tex]f(x) = {x}^{2} [/tex]
If we shift to the right by 1 unit, the function becomes:
[tex]f(x) = {(x - 1)}^{2} [/tex]
If we stretch by a factor of 5, the function becomes,
[tex]f(x) =5 {(x - 1)}^{2} [/tex]
Finally reflecting over the x-axis gives:
[tex]f(x) = - 5 {(x - 1)}^{2} [/tex]
Answer:
f'''(x)=-5(x-1)^2
Step-by-step explanation:
Given:
f(x)= x^2
Shifting 1 unit to right means subtracting 1 from the function i.e
f(x-1)=(x-1)^2
f'(x)=(x-1)^2
now vertically stretching above f'(x) by a factor of 5:
5f'(x)=5(x-1)^2
f''(x)=5(x-1)^2
finally reflecting above f'''(x) over the x-axis:
-f''(x)=-5(x-1)^2
f'''(x)=-5(x-1)^2 !
Find the distance between the points (0, –4) and (–6, 7)
Answer:
12.53
Step-by-step explanation:
x = x₂ - x₁ = -6 - 0 = -6
y = y₂ - y₁ = 7 - (-4) = 11
We can use the Pythagorean theorem to calculate the distance.
z² = (-6)² + 11² = 36 + 121 = 157
z = √157 ≈ 12.53
The distance between the two points is 12.53.
what is the quotient in long divison of 806÷6
Answer:
The quotient to the problem 806 ÷ 6 is 134.3333 and so forth.
The quotient of the expression 806 ÷ 6 will be 134.33.
What is Division method?
Division method is used to distributing a group of things into equal parts.
Given that;
The expression is,
806 ÷ 6
Now, Solve the expression by using long division as;
6 ) 806 ( 134.333.....
- 6
---------
20
- 18
-----------
26
- 24
-------
20
- 18
-------
2
Thus, The quotient of the expression 806 ÷ 6 will be 134.33.
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Find the equation of the line with Slope = 6 and passing through (7,49). Write your equation in the form y=mx+b
y= ?
Using the slope-intercept form, the equation of the line with slope 6 passing through the point (7,49) is obtained as y = 6x + 7.
Explanation:To find the equation of a line given the slope and a point it passes through (7,49), we'll use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Since we are given the slope to be 6, we can substitute this into the equation, getting y = 6x + b. To find b, the y-intercept, we substitute the coordinates of the given point into the equation: 49 = 6(7) + b. After solving, we get b = 49 - 42, which simplifies to b = 7. Therefore, the complete equation of the line is y = 6x + 7.
Find x if f(x) = 2x + 7 and f(x) = -1
f(x) = 2x + 7 and f(x) = -1
Replace f(x) with -1:
-1 = 2x +7
Subtract 7 from both sides:
-8 = 2x
Divide both sides by 2:
x = -8 /2
x = -4
PLS ANSWER IM GIVING 25 POINTS + Brainliest
The following box plot shows the number of years during which 40 schools have participated in an interschool swimming meet:
A box and whisker plot is drawn using a number line from 0 to 10 with primary markings and labels at 0, 5, 10. In between two primary markings are 4 secondary markings. The box extends from 1 to 6 on the number line. There is a vertical line at 3.5. The whiskers end at 0 and 8. Above the plot is written Duration of Participation. Below the plot is written Years.
At least how many schools have participated for more than 1 year and less than 6 years?
4
8
10
20
Answer:
he correct answer is 4.
Step-by-step explanation:
Answer:
The correct answer is 20.
Step-by-step explanation:
Can I get brainliest?
expand and simplify 3(2x+1)+2(x+3)
The required simplified solution of the given expression is 8x + 9.
Given that,
To determine the simplified solution of the expression 3(2x+1)+2(x+3).
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let,
y = 3(2x+1)+2(x+3)
y = 6x + 3 + 2x + 6
y = 8x + 9
Thus, the required a simplified solution of the given expression is 8x + 9.
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Lu-yin predicts that 80% of the people she invites to her party will come. If she wants to have at least 20 guests, how many people should she invite to her party?
Answer:
25
Step-by-step explanation:
Since she predicts that 80% of the invited people come, she needs to invite a number greater than 20, so that 80% of that number is 20.
Let the number of invited people be x.
80% of x must be 20.
80% * x = 20
0.8x = 20
Divide both sides by 0.8
x = 25
Answer: She should invite 25 people.
Check: Let's find 20% of 25. If it is 20, then 25 is correct.
80% of 25 = 0.8 * 25 = 20
Since 80% of 25 is 20, the answer, 25, is correct.
Answer:
80/100=.80
.80x=20
x=25
Step-by-step explanation:
Look at the table. Make a conjuncture about the sum of the first 30 positive even numbers
Answer:
The conjecture is that the sum is [tex]30^2+30=930[/tex].
Step-by-step explanation:
I don't see your table... but let's see if we can make a conjecture about the sum of the first 30 positive even numbers.
What is the sum of the first even number? 2=2
What is the sum of the first two even numbers? 2+4=6
What is the sum of the first three even numbers? 2+4+6=12
What is the sum of the first four even numbers? 2+4+6+8=20
What is the sum of the first five even numbers? 2+4+6+8+10=30
What is the sum of the first six even numbers? 2+4+6+8+10+12=42
Alright, let's stop there for a second.
So we have the following sequence of numbers to find a pattern for:
2,6,12,20,30,42,...
Let's look at the common differences:
6-2 , 12-6 , 20-12 , 30-20, 42-30,...
4 , 6 , 8 , 10 , 12
No common difference here so let's move on too the second common differences:
6-4 , 8-6, 10-8, 12-10
2 , 2 , 2 , 2
So there is a 2nd common difference which means the pattern is a quadratic.
So our expression is of the form [tex]ax^2+bx+c[/tex]
Let's plug in our numbers to come up with a system to solve:
If x=1 , then [tex]ax^2+bx+c=2[/tex]
That is, [tex]a(1)^2+b(1)+c=2[/tex] .
Simplifying this gives: [tex]a+b+c=2[/tex].
If x=2, then [tex]ax^2+bx+c=6[/tex]
That is, [tex]a(2)^2+b(2)+c=6[/tex]
Simplifying this gives: [tex]4a+2b+c=6[/tex].
If x=3, then [tex]ax^2+bx+c=12[/tex]
That is [tex]a(3)^2+b(3)+c=12[/tex]
Simplifying this gives: [tex]9a+3b+c=12[/tex].
So we have this system of equations:
a+ b+ c=2
4a+2b+ c=6
9a+3b+ c=12
I'm going to set this up as a matrix:
[ 1 1 1 2 ]
[4 2 1 6 ]
[9 3 1 12]
Multiply first row by -4:
[ -4 -4 -4 -8 ]
[ 4 2 1 6 ]
[ 9 3 1 12]
Add equation 1 to 2:
[ -4 -4 -4 -8]
[ 0 -2 -3 -2]
[ 9 3 1 12]
Divide first row by -4:
[ 1 1 1 2]
[ 0 -2 -3 -2]
[9 3 1 12]
Multiply top row by -9:
[-9 -9 -9 -18]
[0 -2 -3 -2]
[ 9 3 1 12]
Add equation 3 to 1:
[0 -6 -8 -6]
[0 -2 -3 -2]
[9 3 1 12]
Multiply the second equation by -3:
[ 0 -6 -8 -6]
[0 6 9 6]
[9 3 1 12]
Add equation 1 to 2:
[0 -6 -8 -6]
[0 0 1 0]
[9 3 1 12]
Let's stop there the second row gives us c=0.
So the first row gives us -6b-8c=-6 where c=0 so -6b-8(0)=-6.
Let's solve this:
-6b-8(0)=-6
-6b-0=-6
-6b =-6
b =1
So we have b=1 and c=0 and we haven't used that last equation yet:
9a+3b+c=12
9a+3(1)+0=12
9a+3+0=12
9a+3=12
9a=9
a=1
So your expression for the pattern is [tex]x^2+x+0[/tex] or just [tex]x^2+x[/tex].
Let's test it out for one of our terms in our sequence:
"What is the sum of the first four even numbers? 2+4+6+8=20"
So if we plug in 4 hopefully we get 20.
[tex]4^2+4[/tex]
[tex]16+4[/tex]
[tex]20[/tex]
Looks good!
Now we want to know what happens when you plug in 30.
[tex]30^2+30[/tex]
[tex]900+30[/tex]
[tex]930[/tex]
If you don't like this matrix way, I can think of something else let me.
write a point slope equation for the line that passes through the point (1,22) & is parallel to the line given by y= 14x-3.
Answer:
y-22=14(x-1)
Step-by-step explanation:
Since we are looking for a line parallel to y=14x-3 then we are looking for a line that has the same slope as y=14x-3.
The slope of y=14x-3 is 14.
So the slope of our line is 14.
So we know our equation is in the form y=14x+b.
We can find b by using a point (x,y) on the line. We know (x,y)=(1,22) is a point on the line we are looking for.
So I'm going to replace x with 1 and y with 22 in the equation y=14x+b giving me
22=14(1)+b
22=14 +b
Subtract 14 on both sides
8=b
The equation of the line is y=14x+8. That is slope-intercept form. I will leave this here just in case you are curious of this.
I was do point-slope form now since that is what your question says.
We know the slope is 14 so m=14.
The point-slope form is y-y1=m(x-x1).
We know (x1,y1)=(1,22) so now we substitute.
y-22=14(x-1)
If f(x) = 4 - x^2and g(x) = 6x, which expression is equivalent to (g-f)(3)?
Answer:
(g-f)(3) = 23
Step-by-step explanation:
f(x) = 4-x^2
g(x) = 6x
we need to find g-f(3)
Put the value of x = 3 in g(x) and f(x) and subtract f(x) from g(x) i.e
(g-f)(3) = g(3) - f(3)
(g-f)(3) = 6(3) - {4-(3)^2}
(g-f) (3)=18-(4-9)
(g-f)(3) = 18-(-5)
(g-f)(3) = 18+5
(g-f)(3) = 23
so, (g-f)(3) = 23
Answer:
23
Step-by-step explanation:
(g-f)(3)=g(3)-f(3)
So we need to find g(3) and f(3). Then subtract.
g(3)=6(3)=18.
f(3)=4-(3)^2=4-9=-5.
(g-f)(3)=g(3)-f(3)=18-(-5)=18+5=23
4x2 + 19x-5
Which two binomials are factors of the trinomial?
Answer:
(4x -1 ) ( x +5 )
Step-by-step explanation:
4x2 + 19x-5
(4x ) ( x )
We need to get -5 The factors are -1 and 5 and 1 and -5
4*5 = 20
so the 5 will be on the outside We do this because we have +19 on the inside
(4x -1 ) ( x +5 )
Lets check
FOIL
4x^2 +20x -x -5 = 4x^2 +19x-5
Answer:
The factors are (4x-1)(x+5).
Step-by-step explanation:
4x^2+19x-5
Break the middle term:
First multiply the coefficient of first term by the constant.
4*5=20
Now find any two numbers whose product = 20 and whose sum is equal to the middle term.
20*1 = 20
20-1 = 19
Now break the middle term:
4x^2+20x-x-5
Now group the first two terms and last two terms:
(4x^2+20x)-(x+5)
Now take the common from each group.
4x(x+5)-1(x+5)
(4x-1)(x+5).
Thus the factors are (4x-1)(x+5).....
James is contemplating an investment opportunity represented by the function A(t)=P(1.06)^t, where P is the initial amount of the investment, and t is the time in years. If James invests $5000, what is the average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20?
Answer:
810.58 dollars per year
Step-by-step explanation:
Ok, so we are given that P=5000, so that makes our function A(t)=5000(1.06)^t .
The average rate of change is really the slope of the line going through (15,y1) and (20,y2).
We can find the corresponding y values by plugging the x's there to A(t)=5000(1.06)^t.
So let's do that:
y1=A(15)=5000(1.06)^(15)=11982.79097
y2=A(20)=5000(1.06)^(20)=16035.67736
Now the slope of a line can be found by using the formula:
(y2-y1)/(x2_x1) or just lining up the points and subtracting vertically and remember y difference goes over x difference.
Like so:
( 15 , 11982.79097 )
- ( 20 , 16035.67736)
---------------------------------
-5 -4052.886391
So the average rate of change is whatever -4052.886391 divided by -5 is.....
which is approximately 810.58 dollars per year.
Answer:
The average rate of change in dollars per year between years 15 and 20 is:
[tex]m=\$810[/tex]
Step-by-step explanation:
First we calculate the profit of the investment for the year 15
So
[tex]P=5000\\t=15[/tex]
[tex]A(15)=5000(1.06)^{15}[/tex]
[tex]A(15)=11982.79[/tex]
Now we calculate the profit of the investment for the year 20
So
[tex]P=5000\\t=20[/tex]
[tex]A(20)=5000(1.06)^{20}[/tex]
[tex]A(20)=16035.68[/tex]
Now the average rate of change m is defined as:
[tex]m=\frac{A(20) - A(15)}{20-15}[/tex]
Therefore:
[tex]m=\frac{16035.68-11982.79}{20-15}[/tex]
[tex]m=\frac{4052.89}{5}[/tex]
[tex]m=\$810.58[/tex]
An electrical tower casts a 120-foot shadow. At the same time, a 10-foot
street sign casts a shadow of 8 feet. What is the height of the tower?
O A. 270 ft
O B. 150 ft
O C. 120 ft
O D. 180 ft
Set up a ratio with the height over the shadow.
Let the height of the tower be X
The ratio of the tower is x/120
The ratio if the sign is 10/8
Set them to equal and solve for x:
x/120 = 10/8
Cross multiply:
8x = 1200
Divide both sides by 8:
x = 1200/8
x =150
The answer is B. 150 ft.
Answer:
B. 150 feet.
Step-by-step explanation:
The tower and the street sign and their shadows form 2 similar triangles.
So the corresponding lengths are in the same ratio, then:
120 / 8 = h / 10 where h is the height of the tower.
8h = 120 * 10
h = 120 * 10 / 8
= 150 feet.
If three or more points lie on a line, they are called collinear points
True or False
Answer:
True
Step-by-step explanation:
The prefix "co" means together, and the base "linear" means line. Therefore co-linear means together on a line
1. Find the value of x
2. Using complete sentences, describe your
Answer:
x = 40
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Consider the triangle on the left and calculate the third angle
Subtract the sum of the 2 angles from 180
third angle = 180° - (75 + 50)° = 180° - 125° = 55°
Consider the triangle on the right
The third angle = 55° ( vertical angles )
Subtract the sum of the 2 angles from 180
x = 180 - (55 + 85) = 180 - 140 = 40
Evaluate the following expression. (8^1)0
Possible Answers are:
0
1
8
Answer:
1
Step-by-step explanation:
(8^1)^0
We know that a^b^c = a^ (b*c)
8^1 ^0 = 8^(1*0) = 8^0 =
Anything raised to the 0 power is 1
=1
100 POINTS PLEASE HELP ASAP
Answer:
AB = 3
Step-by-step explanation:
Since AB is a perpendicular bisector then Δ is isosceles and AD = AC, that is
4x - 1 = 2x + 3 ( subtract 2x from both sides )
2x - 1 = 3 ( add 1 to both sides )
2x = 4 ( divide both sides by 2 )
x = 2
Hence AB = x + 1 = 2 + 1 = 3
Answer:
AB=3
Step-by-step explanation: