use the pythagorean theorem to see if the measurements create a right trinangle.
remember the addition of the squared shorter sides must be equal to the largest side squared
[tex]a^2+b^2=c^2[/tex][tex]5^2+12^2=13^2[/tex][tex]\begin{gathered} 5^2+12^2=169 \\ 13^2=169 \\ \\ 169=169 \end{gathered}[/tex]A swimming pool is in the form of a semicircular
The walk surrounding the pool has an area of 336.66 [tex]ft^{2}[/tex] .
A = ( Area of semicircle including side walk ) - ( Area of semicircle without side walk )
radius of smaller semicircle = 10 ft and radius of larger semicircle = 10 + 3 = 13 ft
A = [ ( 3.14 * [tex]13^{2}[/tex] ) / 2 ] - [ ( 3.14 * [tex]10^{2}[/tex] ) / 2 ]
= ( 530.66 - 314 ) / 2
= 108.33 [tex]ft^{2}[/tex]
Since we take walk on both sides , we will multiply it with 2
A = 2 * 108.33
A = 216.66[tex]ft^{2}[/tex]
One side of bigger rectangle = 20 + 3 + 3 = 26 ft
A = area of rectangle - area of square
A = ( 26 * 20 ) - [tex]20^{2}[/tex]
A = 120 [tex]ft^{2}[/tex]
Therefore ,
A = 216.66 + 120
A = 336.66 [tex]ft^{2}[/tex]
Hence , the walk surrounding the pool has an area of 336.66 [tex]ft^{2}[/tex] .
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which equation describes the line with a slope of 2/3 that passes through the point
Option (a)
Given:
The value of slope is, m = -2/3.
Pass throught he point, (x1, y1) = (2,-3)
The objective is to find the equation of the line.
The general equation of straight line is,
[tex]y-y_1=m(x-x_1)[/tex]Now, substitute the given values in the above equation.
[tex]\begin{gathered} y-(-3)=-\frac{2}{3}(x-2) \\ y+3=-\frac{2}{3}(x-2) \end{gathered}[/tex]Hence, option (a) is the correct answer.
how many five letter codes can be made if no letter can be used twice
The aritmetic sequence has the characteristic that each term is the term before plus a constant number. Then we can create the following system of equations:
[tex]\begin{gathered} x-34=p \\ 345-p=x \end{gathered}[/tex]where p is the constant value which is added in each term, and x the number between 34 and 345. If we replace the value of "x" from the second equation into the first one:
[tex]\begin{gathered} 345-p-34=p \\ 311=2p \\ 155.5=p \end{gathered}[/tex]Finally, the term betwen 34 and 345 is 34+p, 189.5
Hence the answer is 189.5
Anza gave Angela directions to her house from school Angela was to head south for 2.2 miles and West for 3.5 miles then South again 45.8 miles use Mental Math to determine how far school is for on this house explain your reasoning
Solution
for this case we can do the following:
Simplify the expression to a polynomial in standard form: (3x + 10) (2x² - 2x + 3)
Step 1
Write out the question.
[tex]\begin{gathered} (3x+10)(2x^2\text{ - 2x + 3)} \\ =3x(2x^2-2x+3)+10(2x^2\text{ - 2x + 3)} \\ =6x^3-6x^2+9x+20x^2\text{ - 20x + 30} \\ =6x^3+14x^2^{}-11x+30^{} \end{gathered}[/tex]You have a combination lock with 3 secret digits. Find the 3 correct digits using the following clues and enter your answer below.
The first clue only tells us that there is one digit that is in the right place, so it could be any one of the following.
The second one tells us that one of the digits is right but in the wrong place, we still cannot confirm if 5 is the number we are talking about.
The fourth clue says that all the numbers are incorrect, so the digits are 2, 5, 0 or 1, now we must find out the correct order.
From clues 3 and 5 we can assume that 0 is one of the digits and that it comes first.
We will discard the number 5 because in clue 3 they talk about 2 correct digits, we already know that 0 is one and we choose 2 instead of the number five because of clues 1 and 2, which talk about only one digit in the correct place but in both of them the 5 remains in the same place.
The 3 digists are: 1, 0 and 2
The correct order is 012
What are the center and the radius of the circle x2−2x+y2=0?A)The center is (1, 0), and the radius is 1.B) The center is (2, 0), and the radius is 2.C)The radius is 0, so the equation cannot represent a circle.D) The radius is negative, so the equation cannot represent a circle.
We want to know the center and the radius of the circle:
[tex]x^2-2x+y^2=0[/tex]We remember that the equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]In this case, we complete the square by adding 1 and substracting 1:
[tex]\begin{gathered} x^2-2x+1+y^2-1=0 \\ x^2-2x+1+y^2=1 \\ \text{Factoring the first three terms, we obtain:} \\ (x-1)^2+y^2=1 \end{gathered}[/tex]This means that the center is the point (1,0), and:
[tex]\text{Radius: }\sqrt[]{1}=1[/tex]In a normal distribution, what percentage of the data falls within 2 standarddeviations of the mean?
In a normal distribution, 68% of data will fall within two standard deviations of the mean
jackie made lunches for the family picnic. Dhe put 8 carrots sticks in each lunch and had no leftovers carrot sticks. which of the following shows how many corrot stick she might have started with?a. 26b. 38c. 44d. 48
Since putting 8 sticks in each lunch box doesn't give any leftover, that means that number of carrot sticks she had is a multiple of 8.
Pretty simply!
Let's see the multiples of 8.
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, ....
Out of the choices, only 48 is a multiple of '8'.
Therefore,
D is correct
If f(x) = 2x² + 1 and g(x)=x²-7, find (f- g)(x).
ANSWER :
(f - g)(x) = x^2 + 8
EXPLANATION :
From the problem, we have :
[tex]\begin{gathered} f(x)=2x^2+1 \\ g(x)=x^2-7 \end{gathered}[/tex](f - g)(x) is the difference between the two functions
That will be :
[tex]\begin{gathered} (f-g)(x)=f(x)-g(x) \\ =2x^2+1-(x^2-7) \\ =2x^2+1-x^2+7 \\ =x^2+8 \end{gathered}[/tex]Martha has 9 feet of red ribbon and 6 feet of green ribbon. How many yards of ribbon does she have altogether?Martha has _____ yards of ribbon.The solution is ______
Since we want the total amount, we first can add the red and green ribbon:
[tex]9+6=15[/tex]Martha has 15 feet of ribbon.
To converto to yards, we can just divide the amount in feet by 3. So, in yards:
[tex]\frac{15}{3}=5[/tex]So
Martha has 5 yards of ribbon.
Jack is buying groceries. He decides to buy 50 total frozen entrees. He buys nothing but Burritos andHungry-Man Meals. The average price of a Hungry-Man Meal is $3.25 while the average price of a Burritois $2.00. If he spends $150 on all the frozen food, how many Hungry-Man Meals and Burritos did he buy?
Let x the total of Hungry-Man Meals bought.
let y the total of burritos bought.
He decides to buy 50 total frozen entrees.
x + y = 50
If we solve the equation for x
x = 50 - y
We also know that he spends $150 on all the frozen food.
Therefore:
x Hungry-Man Meals for $3.25
y burritos for $2.00
x(3.25) + y(2.00) = 150
3.25x + 2.00y = 150
Now substituting 50-y from the first equation into the second equation and solve for y:
3.25x + 2.00y = 150
3.25(50-y) + 2.00y = 150
3.25*50 - 3.25*y + 2.00y = 150
162.5 - 3.25y + 2.00y = 150
162.5 - 1.25y = 150
Subtract both sides by 150
162.5 - 150 - 1.25y = 150-150
12.5 -1.25y = 0
Add both sides 1.25y
12.5 -1.25y+1.25y= 0+1.25y
12.5 +0 = 1.25y
Divide both sides by 1.25
12.5/1.25 = 1.25y/1.25
10 = y
Substitute 10 for y in the result of the x equation:
x = 50 - y
x = 50- 10
x = 40
So 40 Hungry-Man meals and 10 burritos Jack bought.
9. Simplify: 7 - 5m - 10m* O 7+ 15m O 7-15m O 7-5m O 7 +5m
1) Simplifying 7 -5m -10m we'll need to combine like terms. So
7 -5m -10m Combine Like terms
7 -15m
2) Given the options, the answer is 7 -15m
Write the exponential function / (x)=-4.2^(1-x) in the form f(x) = ab^x
Given the equation of the function f(x):
[tex]f(x)=-4\cdot2^{(1-x)}[/tex]We will use the following rules of the exponents:
[tex]\begin{gathered} a^{m+n}=a^m\cdot a^n \\ a^{-m}=\frac{1}{a^m} \\ a^{mn}=(a^m)^n \end{gathered}[/tex]So, we can rewrite f(x) as follows:
[tex]\begin{gathered} f(x)=-4\cdot2^{(1-x)} \\ f(x)=-4\cdot2^1\cdot2^{-x} \\ f(x)=-4\cdot2\cdot(2^{-1})^x \\ \\ f(x)=-8\cdot(\frac{1}{2})^x \end{gathered}[/tex]So, the answer will be option B
please help me solve.I answered this 1808.64 but it is incorrect.
Answer
Surface area = 2260.8 cm²
Explanation
The surface area of a normal sphere is given as
Surface area = 4πr²
where,
π = pi = 3.14
r = radius of the sphere = 12 cm
But this sphere has the middle of the sphere as part of the surface too
Surface area = 4πr² + πr² = 5πr²
Surface area = 5 (3.14) (12²)
Surface area = 2260.8 cm²
Hope this Helps!!!
okay i just need the answer no explanation i just need to find the answer asap
Hello there. To solve this question, we need to pay attention to the data given by the question and set up an equation for the amount of rabbits in that colony.
In the year 2000 there were 1200 rabits in a colony, and it was observed that their population was increasing at a rate of 21% each year
For this type of question, we call f(x) the function that shows the population in a certain time x.
This function varies directly to the initial population and grows exponentially according to the rate .
Thus, we have that f(x) = P0 * (1+r)^x
In this case, P0 = 1200 and r = 0.21 (21% converted into decimals)
f(x) = 1200 * (1 + 0.21)^x
f(x) = 1200 * 1.21^x
This is the function that models the population of this colony for a year x.
To find how many rabbits you'll have in the year 2007, plug in x = 7
f(7) = 1200 * 1.21^7
Calculate the value
f(7) = 1200 * 3.797 = 4556
In which year will the population be equal to 5000
Making f(x) = 5000, we solve for x
5000 = 1200 * 1.21^x
Divide both sides of the equation by 1200
25/6 = 1.21^x
Take the natural log on both sides of the equation
ln(25/6) = ln(1.21^x)
Apply the logarithm power rule: log(a^b) = b * log(a)
ln(25/6) = x * ln(1.21)
Rewriting 1.21 as 121/100 = (11/10)², we get:
ln(25/6) = 2x * ln(11/10)
Divide both sides of the equation by a factor of 2ln(11/10)
x = ln(25/6)/(2ln(11/10)) approx. 7.4867 years
Rounding up to the next year, x = 8 years.
What other number is a part of this fact family? 3,4,
The other number that is a part of the fact family of 3,4 is 7.
According to the question,
We have the following information:
Two numbers of the fact family is 3 and 4.
Now, we know that in a fact family, if two numbers are given then the third number can be found by adding the two given numbers.
(More to know: fact family is often used to prove commutative property of addition. It can be used to find any number of other numbers of fact family are given.)
4+3 = 3+4 = 7
Hence, the other number that is a part of the fact family of 3,4 is 7.
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Rewrite the following into equivalent expressions using the GCF of both numbers and the distributive property.When complete, evaluate the expressions to check for equivalency.124 + 36
24 + 36
[tex]\begin{gathered} \text{factors of 24 = }\mleft\lbrace1,2,3,4,6,8,12,24\mright\rbrace \\ \text{factors of 36 = }\mleft\lbrace1,2,3,4,6,9,12,18,36\mright\rbrace \\ \text{GCF}=12 \\ 24=12\times2 \\ 36=12\times3 \\ (12\times2)+(12\times3) \\ 24+36=12(2+3) \end{gathered}[/tex]The equations in the red box I need to use substitution. Explaining the steps as I go.
We are given the following system of equations:
[tex]\begin{gathered} y=-x^2+63x-790,(1) \\ y=3x+10,(2) \end{gathered}[/tex]We will substitute the value of "y" from the first equation into the second equation:
[tex]-x^2+63x-790=3x+10[/tex]Now we subtract "3x" from both sides:
[tex]-x^2+63x-3x-790=10[/tex]Adding like terms:
[tex]-x^2+60x-790=10[/tex]Now we subtract 10 from both sides:
[tex]-x^2+60x-790-10=0[/tex]Adding like terms:
[tex]-x^2+60x-800=0[/tex]Now we multiply by -1 on both sides of the equation:
[tex]x^2-60x+800=0[/tex]Now we factor in the left side. We need two numbers that when multiplied the product is 800 and their algebraic sum is -60. Those numbers are -40 and -20. Therefore, we get:
[tex](x-40)(x-20)=0[/tex]Now we set each factor to zero:
[tex]\begin{gathered} x-40=0 \\ x=40 \end{gathered}[/tex]For the next factor:
[tex]\begin{gathered} x-20=0 \\ x=20 \end{gathered}[/tex]These are the two values of "x" for the solution. To get the corresponding value of "y" we substitute in the second equation. Substituting the first value we get:
[tex]\begin{gathered} y=3(40)+10 \\ y=120+10 \\ y=130 \end{gathered}[/tex]Now we substitute the second value:
[tex]\begin{gathered} y=3(20)+10 \\ y=60+10 \\ y=70 \end{gathered}[/tex]Therefore, the solutions of the system are:
[tex]\begin{gathered} (40,130) \\ (20,70) \end{gathered}[/tex]can u help me with work?
the x-intercepts are all the x coodinates in which the function will be equal to 0
to find the x intercepts equal the equation to 0
[tex]f(x)=3\cdot(x-6)\cdot(x+4)[/tex]equal all factors involving the x to 0 because if there is any factor equal to 0 then the product between of al products will be 0 as well
[tex]\begin{gathered} 0=3\cdot(x+4)\cdot(x-6) \\ x+4=0 \\ x-6=0 \end{gathered}[/tex]solve both of the equations
[tex]\begin{gathered} x=-4 \\ x=6 \end{gathered}[/tex]the x-intercepts will be
(-4,0) & (6,0)
Listed are the fractions of the total number of books Allisa put in a bookcase 2/5 history books 1/3 math books 1/10 art books Allisa will fill the remainder of the bookcase with science books Drag and drop the fractions into the boxes that show the fraction of the total number of books that are history, math, or art books in the bookcase and the fraction of the total number of books that will be science
Answer:
Books in Bookcase = 5/6
Science Books = 1/6
Explanation:
Given:
Total number of books Alissa put in a bookcase;
2/5 history books
1/3 math books
1/10 art books
We can go ahead and determine the fraction of the total number of books that are history, math, or art books in the bookcase by adding the given fractions together as seen below;
[tex]\frac{2}{5}+\frac{1}{3}+\frac{1}{10}=\frac{12+10+3}{30}=\frac{25}{30}=\frac{5}{6}[/tex]So the fraction of the total number of books that are history, math, or art books in the bookcase is 5/6
Let x represent the fraction of the total number of books that will be science.
We can go ahead and determine the value of x by subtracting the fraction of the total number of books that are history, math, or art books in the bookcase from 1;
[tex]x=1-\frac{5}{6}=\frac{6-5}{6}=\frac{1}{6}[/tex]So the fraction of the total number of books that will be science is 1/6
Which interval notation represents a function white a range of all real numbers greater than -2 and less than 4?A.) -2
range = ? -2 < y < 4 According to the directions this is the inequality
Letter A is the right answer
3(x+2) = 4(x+1)Who can help me
First, we have to solve the parentheses, by applying distributive property:
[tex]3(x)+3(2)=4(x)+4(1)[/tex][tex]3x+6=4x+4[/tex]Add and subtract alike terms:
[tex]6-4=4x-3x[/tex][tex]2=x[/tex][tex]x=2[/tex]The product of two positive consecutive odd integers is 195. Create and solve an equation to find the value of the integers. What is the sum of the two integers?
Let's define the next variables:
x: the first odd integer
y: the next odd integer
Since they are consecutive:
x + 2 = y
The product of them is 195, then:
x*y = 195
Replacing the y from the first equation into the second one:
x*(x + 2) = 195
x*x + x*2 - 195 = 0
x² + 2x - 195 = 0
Solving with help of the quadratic formula:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{-2\pm\sqrt[]{2^2-4\cdot1\cdot(-195)}}{2\cdot1} \\ x_{1,2}=\frac{-2\pm\sqrt[]{784}}{2} \\ x_1=\frac{-2+28}{2}=13 \\ x_2=\frac{-2-28}{2}=-15 \end{gathered}[/tex]Given that we are only interested in positive integers, the solution x = -15 is discarded.
Therefore, the integers are 13 and 15
The sum of them is 13 + 15 = 28
What is the product of 3x2 and 2xºy+5xy4?
SOLUTION
[tex]\begin{gathered} 3x^2(2x^3y+5xy^4) \\ 3x^2(2x^3y)+3x^2(5xy^4) \\ 6x^5y+15x^3y^4 \end{gathered}[/tex]So the first option is the correct answer
change percent to decimal 1,175%
The percentage can be changed to decimal as,
[tex]\begin{gathered} 1175\text{ Percent=}\frac{1175}{100} \\ =11.75 \end{gathered}[/tex]Thus, the required decimal is 11.75.
Could you help me find the slope of the line below
Explanation
[tex]m=\frac{6-(-4)}{6-1}=\frac{10}{5}=2[/tex]Answer
A. 2
Select ALL the correct answers.Identify the two tables which represent quadratic relationships.A. x 0 1 2 3y -4 -8 -10 -10B. x 0 1 2 3y 3 4 5 6C. x 0 1 2 3y -2 -4 -8 -16D. x 0 1 2 3y 4 -4 -4 4E. x 0 1 2 3y 1 2 4 8F. x 0 1 2 3y -2 0 2 4
Step 1
The meaning of QUADRATIC EQUATION is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.
Step 2
We are required to Identify the two tables which represent quadratic relationships.
In a quadratic equation, we have a polynomial in x with degree 2. Hence the result in y or P(x) do get repeated as a polynomial contains x² in it.
Looking at the tables we will observe that;
[tex]\begin{gathered} option\text{ B follows a sequence and is linear} \\ \end{gathered}[/tex][tex]Option\text{ E is not quadratic but exponential}[/tex][tex]Option\text{ F is not right}[/tex]The answers will be;
[tex]Option\text{ D and option A}[/tex]Justine is trying to read the most pages of all students in her Language Arts class by the end of the year. The table shows the pages Justine read, and the time she read them in.Which of the following would be the best equation for the function of the values for Justine's reading?A.h = 40pB.p = 7hC.40p = hD.p = 40h
Given
Hours (h) = 1, 2, 3, 4, 5, 6, 7
Pages (p) = 40, 80, 120, 160, 200, 240, 280
Procedure
[tex]\begin{gathered} \frac{\text{pages}}{\text{hours}}=\frac{40}{1}=\frac{80}{2} \\ \frac{p}{h}=40 \\ p=40h \end{gathered}[/tex]
The answer would be p = 40h
4x = 2 + 14, A = -3 b=3 C = -3 D = 4
4x = 2 + 14
4x = 16
4 is multiplying on the left, then it will divide on the right
x = 16/4
x = 4