Perimeter of an octagon
radius R = 19.9 cm
then To find perimeter
Multiply 8 times lenghts of octagon
with height=
internal angle is= 360/8 = 45°
Now apply rule of Sines
then sin 45/ lside = sin ( 180-45)/2/ radius
Therefore
Lside = sin 45• (19.9) / sin (67.5) = 15.23 cm
Now multiply 8 times this lenght side to find perimeter
8x 15.23 = 121.84 cm
One number is 8 more than another. Their product is -16.
Answer:
The two numbers are 4 and -4
Step-by-step explanation:
Turn the words into equations: let's assign one number to be x and the other to be y
x+8=y
x*y=-16
To solve, substitute the value of y in the first equation into y in the second equation.
This gives x*(x+8)=-16
Simplifying gives x^2+8x=-16
x^2+8x+16=0
(x+4)^2=0
x=-4
plug this value of x back into the first equation, -4+8=y, y is 4
Now to make sure the answer is correct: 4 is 8 more than -4, and 4*-4 does equal 16
f(x)=9-x^2Average rate of change x=0 to x=3x=-1 to x=5x=-2 to ×=2
f(x)=9-x^2
Average rate of change
x=0 to x=3
x=-1 to x=5
x=-2 to ×=2
we know that
The average rate of change is equal to
[tex]\frac{f\mleft(b\mright)-f(a)}{b-a}[/tex]Part 1) we have
a=0
b=3
f(a)=f(0)=9-(0)^2=9
f(b)=f(3)=9-(3^2)=0
substitute the given values in the expression above
[tex]\frac{0-9}{3-0}=-\frac{9}{3}=-3[/tex]the rate of change is -3
Part 2) we have
a=-1
b=5
f(a)=f(-1)=9-(-1)^2=8
f(b)=f(5)=9-(5)^2=-16
substitute the given values in the expression above
[tex]-\frac{16-8}{5-(-1)}=\frac{8}{6}=\frac{4}{3}[/tex]the rate of change is 4/3
Part 3) we have
a=-2
b=2
f(a)=f(-2)=9-(-2)^2=5
f(b)=f(2)=9-(2)^2=5
substitute
[tex]\frac{5-5}{2-(-2)}=\frac{0}{4}=0[/tex]the rate of change is zero
4x + 5y = 19 8x - 6y = -10
Given the system of equations :
[tex]\begin{gathered} 4x+5y=19\rightarrow(1) \\ 8x-6y=-10\rightarrow(2) \end{gathered}[/tex]Multiply the first equation by -2:
[tex]\begin{gathered} -2\cdot4x+(-2)\cdot5y=-2\cdot19 \\ -8x-10y=-38\rightarrow(3) \end{gathered}[/tex]Add the equations (2) and (3) to eliminate x :
[tex]\begin{gathered} 8x-8x-6y-10y=-10-38 \\ -16y=-48 \\ \\ y=\frac{-48}{-16}=3 \end{gathered}[/tex]Substitute with y in equation (1) to find x :
[tex]\begin{gathered} 4x+5\cdot3=19 \\ 4x+15=19 \\ 4x=19-15 \\ 4x=4 \\ \\ x=\frac{4}{4}=1 \end{gathered}[/tex]So, the solution of the system is :
[tex]\begin{gathered} x=1 \\ y=3 \\ (x,y)=(1,3) \end{gathered}[/tex]Due NOW HELP BRAINIEST IF RIGHT
Angles X and Y are supplementary. Angle X measures 115.75° and angle Y measures (m − 8)°. Find m∠Y.
136.5°
128.5°
72.25°
64.25°
The value of m is 72.25° and value of ∠Y = 64.25
if two angles are supplementary, sum of their values will be equal to 180°
∴∠ X + ∠Y = 180°
∠X = 115.75°
∠Y = (m-8)°
∴ 115.75 + ∠ Y = 180°
∠Y = 64.5°
m-8 = 64.5°
m = 72.25°
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The value of [tex]m\angle Y[/tex] is [tex]64.25^o[/tex].
In the give question,
Angles [tex]X[/tex] and [tex]Y[/tex] are supplementary.
Angle [tex]X[/tex] measures [tex]115.75^o[/tex] and angle [tex]Y[/tex] measures [tex](m-8)^o[/tex].
We have to find [tex]m\angle Y[/tex].
We firstly learn about supplementary angel.
Angles that add up to [tex]180[/tex] degrees are referred to as supplementary angles.
As given that [tex]X[/tex] and [tex]Y[/tex] are supplementary so the sum of angle [tex]X[/tex] and [tex]Y[/tex] equals to [tex]180^o[/tex].
[tex]\angle X+\angle Y=180^o[/tex]
As we know that [tex]\angle X=115.75^o, \angle Y=(m-8)^o[/tex]
Now putting the value
[tex]115.75^o+(m-8)^o=180^o[/tex]
Now simplifying the expression.
[tex]115.75^o+m^o-8^o=180^o[/tex]
[tex]107.75^o+m^o=180^o[/tex]
Subtract [tex]107.75^o[/tex] on both side
[tex]107.75^o+m^o-107.75^o=180^o-107.75^o[/tex]
[tex]m^o=72.25^o[/tex]
We have to find the value of [tex]m\angle Y[/tex].
The given value of [tex]Y[/tex] is
[tex]m\angle Y=(m-8)^o[/tex]
Now putting the value of [tex]m[/tex]
[tex]m\angle Y=(72.25-8)^o[/tex]
[tex]m\angle Y=64.25^o[/tex]
Hence, the value of [tex]m\angle Y[/tex] is [tex]64.25^o[/tex].
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How do I solve one-variable inequalities with fractions and parentheses?
Given:
[tex]6x\text{ + }\frac{1}{4}(4x\text{ + 8) > 12}[/tex]First, let's open the bracket:
[tex]\begin{gathered} 6x\text{ + }\frac{1}{4}\times\text{ 4x + }\frac{1}{4}\times8\text{ > 12} \\ 6x\text{ + x + 2 > 12} \end{gathered}[/tex]Collect like terms:
[tex]\begin{gathered} 6x+x\text{ > 12 - 2} \\ 7x\text{ > 10} \end{gathered}[/tex]Divide both sides by 7:
[tex]\begin{gathered} \frac{7x}{7}\text{ > }\frac{10}{7} \\ x\text{ > }\frac{10}{7} \end{gathered}[/tex]Solution:
x > 10/7
Can you help me with this test I got I can give you all the info you need.
Given data:
The given radius is JK=JM=3.
The given length is LM=2.
The tangent is always perpendicular to the radius, the expression for the Pythagoras theorem is,
[tex]\begin{gathered} (JK)^2+(KL)^2=(JL)^2 \\ (JK)^2+(KL)^2=(JM++ML)^2 \end{gathered}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} (3)^2+(KL)^2=(3+2)^2 \\ 9+(KL)^2=25 \\ (KL)^2=16 \\ KL=4 \end{gathered}[/tex]Thus, the first option is correct.
Change 64 square metres into square millimetres.
Give your answer in standard form.
Answer:
64,000,000
Step-by-step explanation:
im smart
triangle ABC has side lengths 10 14 and 26 do the silence form a Pythagorean triple explain
Solution:
Given the side lengths of a triangle ABC;
[tex]a=10,b=14,c=26[/tex]The side lengths form a Pythagorean triple if ithe square of the longest side is equal to the sum of squares of the remaining two sides.
Thus;
[tex]\begin{gathered} 10^2+14^2=100+196 \\ \\ 10^2+14^2=296 \\ \\ 296\ne29^2 \\ \\ \text{ Thus;} \\ \\ 10^2+14^2\ne26^2 \end{gathered}[/tex]Hence, they do not form a Pythagorean triple.
CORRECT OPTION: (B) No, they do not form a Pythagorean triple.
[tex]10^{2}+14^{2}\ne26^{2}[/tex]
Identify the information given to you in the application problem below. Use thatinformation to answer the questions that follow on Practical Domain and PracticalRange.Round your answers to two decimal places as needed.The cost to fill your motor home's propane tank is determined by the functionC(9) = 3.37g where C is the output (cost in $) and g is the input (gallons of gas).The propane tank can hold a maximum of 17 gallonsIdentify the practical domain of this function by filling in the blanks below.Minimum Gallons Purchased 59 s Maximum Gallons PurchasedPractical Domain:
Solution:
The cost to fill the propane tank is modeled by the function;
[tex]\begin{gathered} C(g)=3.37g \\ \\ \text{ Where }C=cost(\text{ \$})\text{ and }g=gallon\text{ \lparen of gas\rparen} \end{gathered}[/tex]The practical domain of this function is;
[tex]0\leq g\leq17[/tex]Hence, the range of this function is;
[tex]\begin{gathered} \text{ Minimum cost:} \\ C(0)=3.37(0) \\ \\ C(0)=0 \\ \\ Maximum\text{ cost:} \\ C(17)=3.37(17) \\ \\ C(17)=57.29 \end{gathered}[/tex]Thus, the practical range is;
[tex]0\leq C(g)\leq57.29[/tex]The function y=f(x)y=f(x) is graphed below. Plot a line segment connecting the points on ff where x=-6x=−6 and x=2.x=2. Use the line segment to determine the average rate of change of the function f(x)f(x) on the interval -6\le x \le 2.−6≤x≤2.
The average rate of change of the function f(x) on the interval−6≤x≤2 is -0.5
This is further explained below.
What is the average rate?Generally, The average rate of reaction is referred to as the change in concentration of any of the reactants or any of the products per unit of time during a specific period of time. This change may occur at any point throughout the reaction.
A single rate is applicable to property that is located in more than one place and that is calculated by weighting the separate rates that are calculated for each location.
In conclusion, The average rate of change on x e(a, b)
[tex]\begin{aligned}m &=\frac{f(b)-f(a)}{b-a} \\\\m &=\frac{f(2)-f(-6)}{2-(-6)} \\\\&=\frac{2-(-(-6))}{8}=\frac{6}{2} \\\\=-0.5\\\\\end{aligned}[/tex]
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Solve for x (Simplify your answer. Type an integer or a decimal. Round to 3 decimal places if needed.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]e^{ln3x}=e^{ln(x+6)}[/tex]STEP 2: Simplify the expression
[tex]\begin{gathered} e^{\ln \left(3x\right)}=e^{\ln \left(x+6\right)} \\ Apply\text{ exponent rules} \\ \ln \left(3x\right)=\ln \left(x+6\right) \\ By\text{ simplification,} \\ x=3 \end{gathered}[/tex]Hence, x = 3
Solve for x.5/6x = 15
The answer is 18
You first multiply both sides by 6 which will make 15, now 90
then divide both sides by 5 so that will make 90, 18 thus x=18 is correct
An aquarium is 26 inches long, 14 inches wide and 24 inches high. The volume of water in the aquarium is 5824 cubic inches. How deep is the water?
The depth of the water is 16 inches.
What is the depth?The depth represents the vertical distance from the bottom of the aquarium to the top of the water level.
The depth can be found by dividing the volume of the water by the area of the aquarium.
The length of an aquarium = 26 inches
The width of the aquarium = 14 inches
The height of the aquarium = 24 inches
The Capacity of the aquarium = 8,736 cubic inches (26 x 14 x 24)
The volume of water in the aquarium = 5,824 cubic inches
The area of the aquarium = 364 squared inches (26 x 14)
The depth of the water in the aquarium = Volume of Water/Area of aquarium
= 16 inches (5,824/364)
Thus, we can conclude that the water is 16 inches deep.
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What was the new balance to start the
next bank statement?
$913.40
$672.40
$554.54
Answer:
Assuming that the amount shown is an addition to the bank account, you add all those and get 2140.34 dollars to start the next statement.
Step-by-step explanation:
Assuming that the amount shown is an addition to the bank account, you add all those and get 2140.34 dollars to start the next statement.
What inequality represents the sentence, the sum of the quotient of a number and 3 and 6 is no more than-12?
We need to split the sentence.
First part, the sum of:
• quotiene of a number and 3
,• and 6
The above could be writen as:
[tex]\begin{gathered} \frac{n}{3}+6 \\ \text{Where n is some number.} \end{gathered}[/tex]The sum above is no more than -12, so the sum is less than -12:
[tex]\frac{n}{3}+6<-12[/tex]The first option is the correct answer.
Express 5√27 in the form n√3, where n is a positive integer.
Answer:
n = 15Step-by-step explanation:
See the steps below:
[tex]5\sqrt{27} =[/tex][tex]5\sqrt{3^2*3} =[/tex][tex]5*3\sqrt{3} =[/tex][tex]15\sqrt{3}[/tex]The value of n is 15.
WILL GIVE BRAINLYEST 200 POINTS!!!1
The range will be impacted by A. The range will increase by 12.
What is a range?A range simply means the difference between the highest and the lowest number.
Highest number = 34
Lowest number = 15
Range = 34 - 15 = 19
When the highest number is 46, the range will be:
= Highest number - Lowest number
= 46 - 15
= 31
The difference will be:
= 31 - 19
= 12
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Answer:
The range will be impacted by A. The range will increase by 12.What is a range?A range simply means the difference between the highest and the lowest number.Highest number = 34Lowest number = 15Range = 34 - 15 = 19When the highest number is 46, the range will be:= Highest number - Lowest number= 46 - 15= 31The difference will be:= 31 - 19= 12
Step-by-step explanation:
Question 2 of 3 Which decimal is equivalent to ( 8 × 3 ) ( 1 10 × 1 10 ) ?
The expression's decimal is equivalent to (B) 0.24.
What do we mean by decimal numbers? A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of whole and partially whole quantities. One of the number types in algebra that has a whole number and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.So, ( 8 × 3 ) ( 1/10 × 1/10 ):
Solve as follows:
(8 x 3) x (1/10 × 1/10)24 x 1/10024/1000.24Therefore, the expression's decimal is equivalent to (B) 0.24.
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The correct question is given below;
Which of the following decimals is equivalent to (8 x 3) (1/10 × 1/10)
A. 0.024
B. 0.24
C. 2.4
D. 24.0
Change this to slope-intercept form. Keep in mind this is in standard form currently.
[tex]\frac{3}{8} x+\frac{2}{3} y=5[/tex]
well, is not exactly in standard form, but close enough.
well, let's take a peek at the denominators, hmmmm 8 and 3, well let's get their LCD hmmm that'd be 24 pretty much, so, let's multiply both sides by the LCD of the denominators, that way we do away with the denominators
[tex]\cfrac{3}{8}x+\cfrac{2}{3}y=5\implies \cfrac{3x}{8}+\cfrac{2y}{3}=5\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{24}}{24\left( \cfrac{3x}{8}+\cfrac{2y}{3} \right)~~ = ~~24(5)} \\\\\\ 9x ~~ + ~~ 16y ~~ = ~~ 120\implies 16y=-9x+120\implies y=\cfrac{-9x+120}{16}[/tex]
[tex]y=\cfrac{-9x}{16}+\cfrac{120}{16}\implies \implies y=-\cfrac{9}{16}x+\cfrac{15}{2} \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
I need help with part A bit if u can help me with every I will give you 5 stars ⭐️ this is my homework
SOLUTION
From the diagram of the box plot
A. The IQR for the male's data is approximately 14 - 5 = 9
B. The median for female is 7
The median for male is estimated 10
Difference 10 - 7 = 3.
C. The mean would be better to compare males with females because from the box plot diagram, more males saw the movie than females.
D. The possible reason for the outlier in the data set could be due to more females attending the movie than normal.
A triangle has a base length of 10 inches and a height of 4 inches
The area of a triangle is 20 inches².
The area of a triangle:
The area of a triangle is equal to half the product of the base and its height.
The formula for the area of a triangle = 1/2 × base × height
Here the base = 10 inches
height = 4 inches
Area = 1/2 × 10 × 4
= 10×2
= 20 inches²
Therefore the area of a triangle is 20 inches².
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Complete the table below by writing the symbols for the cation and anion that make up each ionic compound. The first row has been completed for you.
The cations and Anions for the given compounds are;
1) CuS: Cation; Cu²⁺ and Anion: Su²⁻
2) (NH₄)₂O; Cation; NH₄⁺ and Anion: O²⁻
3)Mn₃(PO₄)₂; Cation; Mn²⁺ and Anion: PO₄³⁻
4) VBr₅; Cation; V⁵⁺ and Anion: Br⁻
How to Identify Anions and Cations?Cations are defined as Positively charged ions that are formed by loss of electrons by an atom. In a cation, number of electrons are less than number of protons.
Anions are defined as Negatively charged ions that are formed by gaining of electron by an atom. In anions, number of electrons are more than the number of protons.
Thus;
1) CuS
Cation; Cu²⁺
Anion: Su²⁻
2) (NH₄)₂O
Cation; NH₄⁺
Anion: O²⁻
3) Mn₃(PO₄)₂
Cation; Mn²⁺
Anion: PO₄³⁻
4) VBr₅
Cation; V⁵⁺
Anion: Br⁻
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write the equation if the following graph (0,2) (4,1)
Step 1: Problem
write the equation if the following graph (0,2) (4,1)
Step 2: Concept
Firstly, find the slope m
Secondly, the intercept c at the vertical axis.
The equation of a line is
y = mx + c
Step 3: Method
[tex]\begin{gathered} \text{Slope m = }\frac{y_2-y_1}{x_2-x_1} \\ (\text{ 0, 2 ) and ( 4, 1 )} \\ x_1=0 \\ y_1\text{ = 2} \\ x_2\text{ = 4} \\ y_2\text{ = 1} \\ m\text{ = }\frac{1\text{ - 2}}{4\text{ - 0}} \\ m\text{ = }\frac{-1}{4} \\ \\ \text{Intercept c = 2} \end{gathered}[/tex]Step 4: Final answer
Substitute m and c in the equation below to find the equation of the line.
y = mx + c
[tex]y\text{ = }\frac{-1}{4}x\text{ + 2}[/tex]Write two linear functions, f(x) and g(x). For example, f(x)=
3x-7-and glx) = -2x+5. Then see whether f(x)= (-g(x)) is equivalent to f(x) + g(x) hint : To find -g(x), just change the signs of all the terms in g(x). Discuss whether you think your results would apply to every function.
The most appropriate choice for functions will be given by -
f (x) - (-g(x)) = f(x) + g(x) holds for f(x)=3x-7-and g(x) = -2x+5.
f (x) - (-g(x)) = f(x) + g(x) holds for every functions
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
For f(x) - (-g(x))
-g(x) = -(-2x + 5)
= 2x - 5
f (x) - (-g(x)) = (3x - 7) - (2x - 5)
3x - 7 - 2x + 5
x - 2
For f(x) + g(x)
f(x) + g(x) = (3x - 7) + (-2x + 5)
= 3x - 7 - 2x + 5
= x - 2
So f (x) - (-g(x)) = f(x) + g(x) holds here
Since addition and subtractions can be done on functions,
f (x) - (-g(x)) = f(x) + g(x) holds for every functions.
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Roberto is charged 0.04% compound interest per day on his credit card purchase of $1200. Find the amount of interest owning after 30 days.
Given:
Assuming 360days in a year and proceeding
[tex]P=\text{ \$1200 ; r=0.04\% ; }t=\frac{1}{12}\text{ years ; n=36}0[/tex][tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]A=1200(1+\frac{0.04}{360})^{360\times\frac{1}{12}}[/tex][tex]A=1200(1.0001)^{30}[/tex][tex]A=1200(1.003)[/tex][tex]A=1203.60[/tex]Amount of interest owning after 30days is $3.60
+3Which of the following is the function f(x) if f'(x) =
f(x) = 8(x -3) (option C)
Explanation:
[tex]f^{-1}(x)\text{ = }\frac{x}{8}+3[/tex]let y = inverse of f(x)
[tex]y\text{ = }\frac{x}{8}+\text{ 3}[/tex]Interchange x and y:
[tex]\begin{gathered} x=\text{ }\frac{y}{8}+\text{ 3} \\ mu\text{ltiply through by 8:} \\ 8(x)\text{ = 8}(\frac{y}{8})+\text{ 3(8)} \\ 8x\text{ = y + 24} \end{gathered}[/tex][tex]\begin{gathered} \text{make y the suject of by subtracting 24 to both sides} \\ 8x\text{ - 24 = y} \\ y\text{ = 8(x - 3) (option C)} \\ f(x)\text{ = 8(x - 3) (option C)} \end{gathered}[/tex]help i don’t know how to do this math problem
Answer:
Given that,
Total surface are=102 m square.
To find the side length of A,
Let the side length of A be a,
we get,
[tex]\text{Total surface area}=102[/tex][tex]18+A+A+6+6+18=102[/tex][tex]48+2A=102[/tex][tex]2A=102-48[/tex][tex]2A=54[/tex][tex]A=27[/tex]One side of the A is 3, we get that
A=product of one side and a
we get,
[tex]A=3\times a[/tex]Substitute for A=27 we get,
[tex]27=3\times a[/tex][tex]a=\frac{27}{3}[/tex][tex]a=9[/tex]The required side length of A is 9 m
Using the following image, if JL=120, what are X,JK, And KL
Given: A-line segment JL=120 units,
[tex]\begin{gathered} JK=4x+6 \\ KL=7x+15 \end{gathered}[/tex]Required: To determine the value of x, JK, and KL.
Explanation: From the given figure, we can write
[tex]JK+KL=JL[/tex]We are now putting the values-
[tex]\begin{gathered} 4x+6+7x+15=120 \\ 11x=120-21 \\ 11x=99 \\ \end{gathered}[/tex]Hence
[tex]x=9[/tex]Now
[tex]\begin{gathered} JK=4x+6 \\ =4\times9+6 \\ =42\text{ units} \end{gathered}[/tex]And
[tex]\begin{gathered} KL=7x+15 \\ =7\times9+15 \\ =78\text{ units} \end{gathered}[/tex]Final Answer: The value of
[tex]\begin{gathered} x=9 \\ JK=42\text{ units} \\ KL=78\text{ units} \end{gathered}[/tex]Write a quadratic equation with a integer coefficients with roots x= 1/2 and x=-4
The quadratic equation with roots a and b is given by:
[tex]x^2-(a+b)x+ab=0[/tex]Here a=1/2 and b=-4.
So the equation is given by:
[tex]\begin{gathered} x^2-(\frac{1}{2}-4)x+(\frac{1}{2})(-4)=0 \\ x^2+\frac{7}{2}x-2=0 \\ 2x^2+7x-4=0 \end{gathered}[/tex]The quadratic equation is as shown above.
help meeee pleasee!!!
thank youu
Answer:
Domain: A, [tex](-\infty, \infty)[/tex]
Range: [tex][4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
