Answers
The logarithm function [tex]\log_ab[/tex], where [tex]a,b>0 \wedge a\not =1[/tex], is increasing for [tex]a\in(1,\infty)[/tex] and decreasing for [tex]a\in(0,1)[/tex]
[tex]\ln x =\log_ex[/tex] and [tex]e\approx 2.7>1[/tex] therefore [tex]\ln x[/tex] is increasing.
Related Questions
In the right triangle ABC shown to the right, what is the length of
AC?
A) 10
B) 14
C) 13
D) 169
E) NOTA
Answers
Answer:
The answer is C) 13.
Step-by-step explanation:
To find the hypotenuse (longest side) of a right triangle, you need to use the Pythagorean Theorem. The formula for the hypotenuse is a^2 + b^2 = c^2.
5^2 (five squared) equals 25, and 12^2 (twelve squared) equals 144.
25 + 144 = 169
Next, find the square root of 169. It is 13. 13 is the length of the hypotenuse.
I hope this helped! :)
In the right triangle ABC, the length of the AC is equal to [tex]13[/tex] units.
What is the right triangle?" Right triangle is defined as a triangle with one of the interior angles with measure equals to [tex]90[/tex] degrees."
Formula used
Pythagoras theorem,
(Hypotenuse)² = ( adjacent side)² + (opposite side)²
According to the question,
In the right triangle ABC,
Adjacent side 'BC' [tex]= 12[/tex] units
Opposite side 'AB' [tex]= 5[/tex] units
'AC' represents the hypotenuse of the right triangle
Substitute the value in the Pythagoras theorem we get,
[tex]AC^{2} = BC^{2} +AB^{2} \\\\\implies AC^{2} = 12^{2} + 5^{2} \\\\\implies AC^{2} = 144 + 25\\\\\implies AC = \sqrt{169} \\\\\implies AC =13units[/tex]
Hence, Option(C) is the correct answer.
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Which equation can be used to solve for b?
Answers
Answer:
The first one
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{b}{8}[/tex]
Multiply both sides by 8
8 × tan30° = b, that is
b = 8tan30°
Answer:
b = (8)tan(30o)
Step-by-step explanation:
The graph of f(x) = |x| is reflected across the x-axis and translated to the right 6 units. Which statement about the domain and range of each function is correct? A)Both the domain and range of the transformed function are the same as those of the parent function.
B(Neither the domain nor the range of the transformed function are the same as those of the parent function.
C)The range but not the domain of the transformed function is the same as that of the parent function.
D)The domain but not the range of the transformed function is the same as that of the parent function.
Answers
Answer:
The domain but not the range of the transformed function is the same as that of the parent function ⇒ answer D
Step-by-step explanation:
* Lets talk about the transformation
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) translated horizontally to the right by h units,
then the new function g(x) = f(x - h)
- The domain of a function is set of the values of x which make
the function defined
- The range is the set values of y that corresponding with the domain
- The domain of the function f(x) = IxI is the set of all real numbers
∴ The domain of f(x) is {x : x ∈ R}
- The range of the function f(x) = IxI is the set of all real numbers
greater than or equal 0
∴ The range f(x) = {y : y ≥ 0}
∵ f(x) reflected across the x-axis, then it will be change to g(x) = -IxI
∴ All the y-coordinates of the point on the function will be change
from positive values to negative values
∵ The rang of f(x) is {y : y ≥ 0}
∴ The range of g(x) is {y : y ≤ 0}
∵ After the reflection the function translated 6 units to the right
∴ The x will change to x - 6
∴ The function will be h(x) = -Ix - 6I
- There is no values of x make h(x) undefined, then its domain is
set of all real number
∴ The domain of h(x) is {x : x ∈ R}
∵ The domain of f(x) is {x : x ∈ R}
∵ The range of h(x) is the same the range of g(x)
∴ The range of h(x) is {y : y ≤ 0}
- f(x) and h(x) have same domains and different ranges
∴ The correct statement is: The domain but not the range of the
transformed function is the same as that of the parent function
- Look to the attached graph for more understanding
# The red graph is f(x)
# The blue graph is h(x)
Answer:
d
Step-by-step explanation:
Which of the following could be the ratio between lengths of the two legs of a 30-60-90 triangle
Answers
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]
How many subsets does the set A have? A={-3,-2,-1,0,1,2,3}
Answers
Answer:
128
Step-by-step explanation:
You find the number of subsets of a set by using the formula [tex]2^{\text{ number of elements}[/tex].
We have 7 elements so that means we have [tex]2^{7}=128[/tex] subsets.
A set with 7 elements can have 128 subsets, as calculated using the equation 2^n, where n is the number of elements in the set.
Explanation:In Mathematics, a subset is a portion of a set, including the empty set and the set itself. The number of subsets a set can have is calculated using the equation 2^n, where 'n' is the number of elements in the set. In this case, the set A includes 7 elements, therefore applying the equation we get: 2^7=128 subsets, which is the answer to your question.
For example, {-3, -1, 0} would be a subset of set A, as would {0, 1, 2}, {-2, 0, 2}, and so on. The complete set ({-3,-2,-1,0,1,2,3}) is also a subset, as is the empty set ({}).
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If three or more points lie on a line, they are called collinear points
True or False
Answers
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
What is cos -1 ( -1/2) in quadrant 1 ?
Answers
Answer:
[tex]\frac{2\pi}{3}[/tex]
Step-by-step explanation:
So here they are asking for one angle that gives you the cosine value is equal to -1/2 while being in quadrant 2.
So you look in quadrant 2 and find x=-1/2 which is at [tex]\frac{2\pi}{3}[/tex].
[tex]\cos^{-1}(\frac{-1}{2})=\frac{2\pi}{3}[/tex] while being in quadrant 2.
Choose the equation that represents a line that passes through points (-6,0) and (2,0).
Answers
Check the picture below.
bear in mind that, horizonta lines are just y = "some constant", and vertical lines are x = "some constant".
Could some please help me with this math question
Answers
Slope intercept form is written in this format:
y=mx+b
m represents the slope
b represents the y intercept
You can clearly see that line intercepts the y axis at -1 so if you substitute that in:
y = mx - 1
You can easily find the slope by following this simple formula: rise/run
If you start at (0, -1) and try to get to (1, 2) then you go up 3 units and across 1 unit so the slope is 3/1 or 3. It’s not a negative slope since the line goes upwards and not downwards.
If you substitute the slope and y intercept you get:
y = 3x - 1
~~hope this helps~~
For this case we have that the equation of a line of the slope-intersection form is given by:[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
To find the slope we look for two points through which the line passes:
We have to:
[tex](x1, y1) :( 1,2)\\(x2, y2): (- 1, -4)[/tex]
Thus, the slope is:
[tex]m = \frac {-4-2} {- 1-1} = \frac {-6} {- 2} = 3[/tex]
We have then:
[tex]y = 3x + b[/tex]
Substituting a point in the equation to find b:
[tex]2 = 3 (1) + b\\2 = 3 + b\\b = 2-3\\b = -1[/tex]
Finally, the equation is:[tex]y = 3x-1[/tex]
Answer:
Option D
Samantha's hockey team is fundraising for a trip to Europe! They are aerating lawns to raise money. Aerating
lawns is a great service for homeowners because it helps the grass grow new roots and absorb water
producing healthier lawns! The team has decided to charge $35/lawn for city-sized lots. The rental cost for two
aerating machines is $215. Samantha's team has planned a Saturday to aerate.
a. Write an equation to relate the fund raised, R, in dollars to the number of lawns, I,
aerated during the day.
b. Samantha's team was able to aerate 26 lawns in one day! How much money did they
raise?
How much money would the team lose if they were unable to aerate due to weather conditions? Is there any
possible way they could avoid this potential loss?
plz help
Answers
Answer:
a)The equation is $35l-$215
b)Amount = $695
c)They will loose $215.
Step-by-step explanation:
From the question you should understand that;
The charge is $35 per lawnThe rental cost for aerating machine is $215The funds raised is the amount gained after aeration work minus the cost of renting the machine.The equation that relates the fund raised and number of lawns aerated during a day is;
Let number of lawns aerated that day be l
The cost to aerate one lawn per day is $35
Cost to rent the aeration machine is $215
a)The equation is ;
[tex]=(l*35)-215[/tex]
= $35l-$215
b)Money raised
number of lawns,l=26
Substitute in the equation
Amount=$35l-$215
=$(35×26)-$215
=$910-$215=$695
c)If the team were unable to aerate due to weather condition, they will incur a loss to to renting of the aeration machine.They will lose $215.This can be avoided by not renting the aeration machine when the weather conditions seems unfavorable for working.
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?
Answers
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.
Simplify 3 sqrt 5x * 3 sqrt 25x^ 2 completely.
Answers
Answer: It’s D
5x
25x can still be simplified all the way down to 5x
(D) 5x Is the correct answer
The radius of the circle whose equation is (x - 3)² + (y + 1)² = 16 is
A). 4
B). 8
C). 16
Answers
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]
Simplify h= 105sin (0.0698(90+1)) + 105
Answers
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]
Find the distance between the points (0, –4) and (–6, 7)
Answers
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.
why is 2 the only number that is always 4 when added multiplied or squared
Answers
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
How many significant figures does this number have? 6,253.862 3 4 7 0
Answers
Answer: 7
Step-by-step explanation: Since there are no 0’s, just count the number of digits. There are 7.
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
Answers
Answer:
he correct answer is 4.
Step-by-step explanation:
Answer:
The correct answer is 20.
Step-by-step explanation:
Can I get brainliest?
If pentagon OPQRS is dilated by a scale factor of seven over four from the origin to create O'P'Q'R'S', what is the ordered pair of point P'?
Answers
Answer:
The ordered pair of P'=(-8.75, 5.25)
Step-by-step explanation:
To get the ordered pair of point P' you simply have to multiply the coordinates of P by scale factor of 7/4
P:(-5,3)
P'(x,y)= (-5* 7/4, 3*7/4)
P'(x,y) = (-35/4 , 21/4)
P'(x,y) = (-8.75, 5.25)..
Thus the ordered pair of P'=(-8.75, 5.25)....
Answer:
(−5.25, −3.5)
Step-by-step explanation:
please help me with this parent function
Answers
Answer:
[tex]\sqrt[3]{x} -3[/tex]: The parent graph will move 3 units down.
[tex]\sqrt[3]{x-3}[/tex]: The parent graph will move 3 units right.
Step-by-step explanation:
The parent function [tex]\sqrt[3]{x}[/tex] looks like the first image attached.
Using knowledge of transformations, numbers outside the radical move the graph up or down (vertically). A positive number moves the graph up; a negative number moves the graph down.
Numbers inside the radical move the graph left or right (horizontally). A positive number moves the graph left; a negative number moves the graph right.
In the first transformation [tex]\sqrt[3]{x} -3[/tex] the number is outside of the radical, meaning that the graph will move vertically. The 3 is negative, so the graph will move 3 units down.
The first transformation moves the parent graph 3 units down.
In the second transformation [tex]\sqrt[3]{x-3}[/tex] the number is inside the radical so the graph will move horizontally. The 3 is negative so the graph will move 3 units to the right.
The second transformation moves the parent graph 3 units right.
The attached images show:
parent function graphparent function graph moved 3 units downparent function graph moved 3 units rightparent function graph and the two transformationscarlene 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
Answers
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.
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
Answers
The answer is option "D. Figure U"
Find x if f(x) = 2x + 7 and f(x) = -1
Answers
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
4x2 + 19x-5
Which two binomials are factors of the trinomial?
Answers
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).....
Give an example of a rational function that has a horizontal asymptote at y = 1 and a vertical asymptote at x = 4.
Answers
Answer:
Possibility 1: [tex]\frac{(x+1)(x+1)}{(x-4)(x+5)}[/tex]
Possibility 2: [tex]\frac{(x+1)(x+3)(x-3)}{x(x-4)(x+5)}[/tex]
Possibility 3: [tex]\frac{-4(x-4)(x+1)}{-4(x-4)(x-4)}[/tex]
There are infinitely many more possibilities.
Step-by-step explanation:
So we are looking for a fraction in terms of x.
We have a horizontal asymptote so that means the degree of the top has to equal to degree of the bottom. It is also at y=1 which means the coefficient of the leading term on top and bottom must be the same (but not zero) since the same number divided by the same number is 1.
Now we also have a vertical asymptote at x=4 which means we need a factor of x-4 on bottom.
So there is a lot of possibilities. Here are a few:
Possibility 1: [tex]\frac{(x+1)(x+1)}{(x-4)(x+5)}[/tex]
You have the degrees are the same on top and bottom and the leading coefficients are the same. You also have that factor of (x-4) on bottom.
Possibility 2: [tex]\frac{(x+1)(x+3)(x-3)}{x(x-4)(x+5)}[/tex]
Possibility 3: [tex]\frac{-4(x-4)(x+1)}{-4(x-4)(x-4)}[/tex]
Now a factor of (x-4) can be canceled here but you still have a factor of (x-4) left on bottom so you still have the vertical asymptote. You also still have the same leading coefficient on top and bottom (-4 in this case) and the same degree.
If f(x) = 4 - x^2and g(x) = 6x, which expression is equivalent to (g-f)(3)?
Answers
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
Express 0.7723 as a fraction.
Answers
Answer:
7033/10000
Step-by-step explanation:
You get his answer by times it by 1000 so the decimal point is out of the number
100 POINTS PLEASE HELP ASAP
Answers
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:
1. Find the value of x
2. Using complete sentences, describe your
Answers
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
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?
Answers
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: