Answer:
288 cm^3
Step-by-step explanation:
First, you have to calculate the volume of your individual bar. To do this, you multiply the three given values, so it would look like 8*3*1=24. This means that your individual bar has a volume of 24 cm^3.
To hold 12 granola bars, this would mean that your volume of the individual granola bar would be multiplied by 12, because that is how many you want to fit inside the box. So your operation would looked like 24*12=288 cm^3
Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. 22 and 15
Answer:
7 < (third side length) < 37
Step-by-step explanation:
Add these two side lengths together. We get 37. Unless the 3rd side is LESS than 37, we cannot form a triangle.
Next, subtract 15 from 22, obtaining 7. The 3rd side has to be GREATER than 7 in order for the sides 7+, 15 and 22 to form a triangle.
7 < (third side length) < 37
Answer:
26.63 ??
Step-by-step explanation:
I think you use pythagorean theorum to solve.
do 22^2 and 15^2 and get 709.1569
sqrt of that is 26.63
[tex]solve for x if 4 x+1-9(2 ^{2} +2=0[/tex]
Answer:
mark my answer as the brainliest
Step-by-step explanation:
x = 53/4
Answer:
4×+1-9 (2^)+2)=0
4×+1-9 (4+2)=0
4×+1(-36-18)=0
4×+1 (-54)=0
4×-54=0
4×=54
×=54÷4
×=13.5
The coordinates of rhombus ABCD are A(–4, –2), B(–2, 6), C(6, 8), and D(4, 0). What is the area of the rhombus? Round to the nearest whole number, if necessary.
Answer:
The rhombus ABCD has an area of 22 square units.
Step-by-step explanation:
The coordinates of rhombus ABCD are shown in the image attached below. The area of the rhombus can be found in terms of their diagonals, which are now calculated by Pythagorean Theorem:
[tex]AC = \sqrt{[6-(-4)]^{2}+[8-(-4)]^{2}}[/tex]
[tex]AC = 15.620[/tex]
[tex]BD = \sqrt{(4-6)^{2}+[0-(-2)]^{2}}[/tex]
[tex]BD \approx 2.828[/tex]
The area of the rhombus is: ([tex]AC = 15.620[/tex] and [tex]BD \approx 2.828[/tex])
[tex]A = \frac{AC\cdot BD}{2}[/tex]
[tex]A = \frac{(15.620)\cdot (2.828)}{2}[/tex]
[tex]A = 22.087[/tex]
The rhombus ABCD has an area of 22 square units.
Answer:
22 units
Step-by-step explanation:
For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4
A. (5+1/2 x)^6
B. (Y- 1/2 x) ^6
C. (5- 1/2 x) ^6
D. (-5 + (- 1/2 x))^6
Answer:
C. [tex](5-\frac{1}{2})^6[/tex]
Step-by-step explanation:
Given
[tex]15(5)^2(-\frac{1}{2})^4[/tex]
Required
Determine which binomial expansion it came from
The first step is to add the powers of he expression in brackets;
[tex]Sum = 2 + 4[/tex]
[tex]Sum = 6[/tex]
Each term of a binomial expansion are always of the form:
[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]
Where n = the sum above
[tex]n = 6[/tex]
Compare [tex]15(5)^2(-\frac{1}{2})^4[/tex] to the above general form of binomial expansion
[tex](a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]
Substitute 6 for n
[tex](a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]
[Next is to solve for a and b]
From the above expression, the power of (5) is 2
Express 2 as 6 - 4
[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]
By direct comparison of
[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]
and
[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]
We have;
[tex]^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4[/tex]
Further comparison gives
[tex]^nC_r = 15[/tex]
[tex]a^{n-r} =(5)^{6-4}[/tex]
[tex]b^r= (-\frac{1}{2})^4[/tex]
[Solving for a]
By direct comparison of [tex]a^{n-r} =(5)^{6-4}[/tex]
[tex]a = 5[/tex]
[tex]n = 6[/tex]
[tex]r = 4[/tex]
[Solving for b]
By direct comparison of [tex]b^r= (-\frac{1}{2})^4[/tex]
[tex]r = 4[/tex]
[tex]b = \frac{-1}{2}[/tex]
Substitute values for a, b, n and r in
[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]
[tex](5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
Solve for [tex]^6C_4[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......[/tex]
Check the list of options for the expression on the left hand side
The correct answer is [tex](5-\frac{1}{2})^6[/tex]
Suppose that f(x)=4x+5. What is f^-1 (f^-1(9)) ?
Step-by-step explanation:
the inverse of the inverse of a function is the function itself
It's like going and coming back
f^-1(f^(-1)9) = f(9) f(9) = 4*9+5f(9) = 36+5 f(9) = 41Answer:
9
Step-by-step explanation:
The inverse of the inverse is the input
f^-1 (f^-1(9)) = 9
As a proof
f(x) = 4x+5
y = 4x+5
Exchange x and y
x = 4y+5
Solve for y
(x+5) = 4y
(x+5)/4 = y
f^-1 (x) = ( x-5)/4
Then find the inverse of this function
y = ( x-5) /4
Exchange x and y
x = (y-5)/4
4x = y-5
4x+5 = y
Which gives us the original function back
f^-1( input) = 4x+5
Using the value given
f^-1 (9) = ( 9-5)/4=4/4 =1
Using the 1 from the previous part as the input
f^-1( 1) = 4*1+5 = 4+5 = 9
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15:115:115, colon, 1. He currently has 404040 grams of the spice blend, and he can go buy more if necessary. He wants to make 101010 servings, where each serving has 757575 grams of rice. Overall, David spends 4.504.504, point, 50 dollars on rice. How many servings can David make with the current amount of spice he has
Answer:
8 servings
Step-by-step explanation:
At the ratio of 15:1, the 75 grams of rice in one serving will require 75/15 = 5 g of spice. David's inventory of 40 g of spice is enough for ...
40 g/(5 g/serving) = 8 servings
Only 8 servings can be made with the available spice.
Rice to spice ratio = 15 : 1
Number of grams per serving = 75 grams
Grams of spice available = 40 grams
Grams of rice, r required for available spice :
15 grams of rice = 1 gram of spice
r grams of rice = 40 grams of spice
Cross multiply :
r = (40 × 15)
r = 600 grams
The grams of rice which can go with the available spice :
Number of servings = grams of rice / grams per serving
Number of serving = 600 grams / 75 grams
Number of grams per serving = 8
Hence, The number of servings which can be made with the available spice is 8 servings
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PLEASE HELPPPP Wilson is thinking about buying a house for $249,000. The table below shows the projected value of two different houses for three years. Number of years 1 2 3 House 1 (value in dollars) 253,980 259,059.60 264,240.79 House 2 (value in dollars) 256,000 263,000 270,000 Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points) Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points) Part C: Wilson wants to purchase a house that would have the greatest value in 45 years. Will there be any significant difference in the value of either house after 45 years? Explain your answer, and show the value of each house after 45 years. (4 points) (10 points)
Part A
House 1: we make exponential can be used to describe the
value of house 1. After 1 year, 253480 = 249000 x 1.02
After 2 years, 259059.6 = 25398×1.02. After 3 years 264240.79 =259059.60x1.02.
House 1: we make linear. 256000=249000 + 1000.263000 = 256000 +7000.270000=263000 + 1000.
Part B.
House 1: f(x)=249000 1.02x [genometic sequence]
House 2: f(X) = 24900 + 1000x [arithmetic progression]
Part C
House 1: f(45)=249000×1.02 45 = 607025.697
House 2: f(45) = 249000 +7000x45 = 564000
"House 1 is an arithmetic sequence that increases in price each year while House 2 is an arithmetic sequence that only increases by 1000 per year.
What are word problems in mathematics?
In computational mathematics, a word problem is a problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.
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what is the average rate of change of f over the interval [-3,9]
Answer:
According to the graph, f(−3)=3 and f(9)=-7
-7-3/9-(-3)= −10/12
Therefore the answer is -5/6
From Khan
The average rate of change over the interval [-3,9] will be 63 units per one unit change in y - value.
What is Polynomial? What are exponents? What is the general equation of a straight line? A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.An exponent is a number that is placed as a superscript over a number. In other words, it indicates that the base is raised to a certain power. Tis expression means that -[tex]b^x = \underbrace{b \times \dots \times b}_{x \text{ times}}[/tex]
The general equation of a straight line is : y = mx + cwhere : [m] → is slope of line and [c] → is the y - intercept
We have the following function -
f(x) = x³ - 9
The average rate of change would be -
r = {720 - (- 36)}/{9 - (- 3)}
r = 756/12
r = 63
Therefore, the average rate of change over the interval [-3,9] will be 63 units per one unit change in y - value.
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[ Complete question -
what is the average rate of change of f(x) = x³ - 9 over the interval [-3,9] ]
15 POINTS!!!!!!!!!!
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k. "Graph of f of x and g of x. f of x equals 1 over 3 x minus 3 and g of x equals 1 over 3 x plus 1. "
a.) 2
b.) 3
c.) 4
d.) 5
Answer: B.
k=3
Step-by-step explanation:
g(x) is 3 units higher than f(x)
so k must be equal to 3
Answer:
it is b i think
k=3
Step-by-step explanation:
Which an equation of a line that has a y-intercept at (0,0) (create your own slope)
Answer:
y = 3x
Step-by-step explanation:
Assume a slope of 3
The y intercept is 0
The slope intercept form of the equation is
y= mx+b where m is the slope and b is the y intercept
y =3x+0
y = 3x
pls asap its not 128......In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answer:
hope it helps
this is my best
please tell me if I'm wrong
please help me immediately
Sandy bought a soft drink for two dollars and five candy bars. She spent
a total of seventeen dollars. How much did each candy bar cost ?
Answer:
3 dolla
Step-by-step explanation:
Which are the roots of the quadratic function f(q) = q? - 125? Select two options.
Oq=515
Oq=-575
Oq=3/5
Oq=-375
Oq=25/5
Answer:
A and C
Step-by-step explanation:
The roots of the quadratic function f(q) = q² - 125 are q = 5 and q = -5.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The quadratic function f(q) = q² - 125 can be factored as (q - 5)(q + 5).
Now,
To find the roots, we set the function equal to zero and solve for q:
So,
q² - 125 = 0
(q - 5)(q + 5) = 0
q - 5 = 0 or q + 5 = 0
q = 5 or q = -5
Therefore,
The roots of the quadratic function f(q) = q² - 125 are q = 5 and q = -5.
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Which of the following best describes the relationship between (x-3) and the
polynomial x3 + 4x2 + 2?
Answer:
c. (x-3) is not a factor.
Step-by-step explanation:
You spend 1/5 of your income on car payment. You spend 3/8 of the remainder of your income on rent. What fraction of income is spent on rent?
Answer:
3/10
Step-by-step explanation:
1/5 of total income - spent on car
remainder income = 4/5
3/8 of remainder = 3/8 ×4/5 = 3/10(of total income spent on rent)
the word "of" means you can find it by multiplication
e.g. 2 of 1/2 means 2 × 1/2 which is 1
Make a 3-by-3 logic grid on your own paper. Use it to help you solve the logic
puzzle and answer the question given below.
Tina, Jewel, and Amy have three different pets (dog, goldfish, and ferret).
• Tina is allergic to dogs.
• Jewel does not have the ferret.
• The dog belongs to Amy.
Who owns the ferret?
Answer:
Tina
Step-by-step explanation:
Since Amy owns the dog, she doesn't have the ferret and we know that Jewel doesn't have the ferret so the answer is Tina.
Write ln (4∕9) in terms of ln 2 and ln 3. Question 13 options: A) 3(ln 2 – ln 3) B) 2ln 2 – 2ln 3 C) 4ln 2 – 4ln 3 D) ln2 2 – 4ln 3
Answer:
The answer is option B
Step-by-step explanation:
2ln 2 - 2ln3
= ln ( 2²/3²)
= ln (4/9)
Hope this helps you
Answer:
B) 2ln 2 – 2ln 3
Step-by-step explanation:
is 3x+4y=12 linear or nonlinear......is y=1/2x+6 linear or nonlinear......is y=4x to the power of 2 linear or nonlinear......is y+2=|4| linear or nonlinear......is y+6=4x linear or nonlinear......
3x+4y=12 is Linear.
y-1/2x+6 is Linear.
y=4x^2 is nonlinear.
y+2=|4| is linear.
y+6=4x is linear.
In order to tell whether an equation is linear or not, you have to first see if there is any variable^2 or more than ^1. If that is the case, it isn't linear. For example the equation x^2=4 or y^5=100 isn't linear. It also isn't linear if the equation is divided by X or Y.For example the equation 1/x=1 isn't linear or 1/y^2=5 isn't linear.
A question is also linear if you can write it in the form y=mx+b , 'm' meaning the slope of the equation and 'b' meaning the y-intercept of the equation.
Which of the following functions represent exponential growth? f(x)=.0001(1.77)^x f(x)=2(1.5)^x/2 f(x)=5(0.5)^-x f(t)=5e^-t
Answer:
Hello There. ☆~\《`°---_●£●__---`°》\~☆
An exponential growth function is represented by
f(x)=a(b)^{x},a>0,b>1.
The given functions can be written as,
A)f(x)=.001(1.77)^x,0.001>0,1.77>1
B)f(x)=2(1.5)^{x/2}=2(\sqrt{1.5} )^x,2>0,\sqrt{1.5} >1
C)f(x)=5(0.5)^{-x}=5(2)^x,5>0,2>1
D) f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e.
So the function f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e violates the conditions for an exponential growth function. It is an exponential decay function.
The correct choices are (A), (B), (C).
Hope It Helps!~ ♡
ItsNobody~ ☆
The functions that represent exponential growth are choices (A), (B), and (C). The correct option is A, B, and C.
What is exponential growth?Exponential growth is the process of gradual increase of quantity over time.
An exponential growth function is represented by
[tex]\rm f(x)=a(b)^{x}[/tex], a>0,b>1
The given functions can be written as,
A)[tex]f(x) = .001(1.77)^x[/tex], 0.001>0,1.77>1
B) [tex]f(x) = 2(1.5)^{x/2} = 2(\sqrt{1.5} )^x,[/tex] 2>0, [tex]\sqrt{1.5}[/tex] >1
C)[tex]f(x) = 5(0.5)^{-x}=5(2)^x[/tex], 5>0, 2>1
D) [tex]f(t) = 5e^{-t}=5(\frac{1}{e} )^x[/tex], 5>0, 1/e.
So, the function [tex]f(t)=5e^{-t}=5(\frac{1}{e} )^x,5 > 0,1/e[/tex] violates the conditions for an exponential growth function. It is an exponential decay function.
The correct choices are (A), (B), and (C).
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What is the measure of the angle between the minute and the hour hands, when they show 3:05 PM?
Answer:
62.5°
Hope this helps :)
What is the range of the function for the given domain? y = 2x − 5 D: {-2, 0, 2, 4}
Answer:
Range of Function : { - 9, - 5, - 1, 4 }
Step-by-step explanation:
We know that y = 2x - 5 provided the domain ( x - values ) { - 2, 0, 2, 4 }. Let us substitute each element in this set of domain as x in the equation "y = 2x - 5" as to solve for the y - values, otherwise known as the range of the function.
{ - 2, 0, 2, 4 }
y = 2( - 2 ) - 5 = - 9,
y = 2( 0 ) - 5 = - 5,
y = 2( 2 ) - 5 = - 1,
y = 2( 4 ) - 5 = 4
We have the set of y - values as { - 9, - 5, - 1, 4 }. This is the range of our function.
A certain clock is losing time. The clock loses 2/15 seconds every minute. How many seconds does the clock lose in one hour?
Answer:
8mins
Step-by-step explanation:
(2x60)/15=8 I hope this helps, hope it's right
Answer:
8 minutes
Step-by-step explanation:
You will multiply 60 times 2 and then divide by 15 leaving you with 8
Question: John and Harry went to a stationery shop. John bought 3 pens and 8 notebooks for $20.50. Harry bought 4 pens and 5 notebooks for $16.00. Identify the cost of a pen and the cost of a notebook. (pen: $1.00 notebook: $2.50) (pen: $2.00 notebook: $1.50) (pen: $1.50 notebook: $2.00) (pen: $2.00 notebook: $3.00)
Answer:
pen: $1.50 notebook: $2.00
Step-by-step explanation:
4×1.50 =6
5×2 = 10
6+10= 16
3×1.50= 4.50
8×2= 16
4.50 + 16 = 20.50
Select the correct answer.
Molly rewrote the equation as shown:
-50 + 11 =8-30
50 +11+30=8-30-30
Which property did she use to rewrite the equation?
[tex]\text{Molly used the addition property of equality}\\\\\text{In the equation shown in the question, you can see that Molly is trying}\\\text{to find the value of "d"}\\\\\text{In order to do this, she must get the "d" variable by itself}\\\\\text{To do this, she adds "3d" to both sides to get the "d" variable on one side}\\\\[/tex]
If the perimeter of a square is 32 meters, then what is
the area of the square, in square meters?
Answer:
The awnser is 64
Step-by-step explanation:
It is 64 because you devide the perimiter (32) by 4, to get all sides, and then multiply 1 side by the other to get 64
THIS METHOD ONLY WORKS FOR A SQUARE
Solve on the interval [0,2pi)
4 CSC x + 1 = -3
Answer:
[tex]$\frac{3\pi }{2}$[/tex]
Step-by-step explanation:
Solve for the interval: [tex][0, 2\pi)[/tex]
[tex]4 \csc(\theta)+1=-3[/tex]
[tex]4 \csc(\theta)=-4[/tex]
[tex]\csc(\theta)=-1[/tex]
[tex]$\frac{1}{\sin(\theta)} =-1 \Rightarrow \sin(\theta)=-1$[/tex]
We have [tex]\sin(\theta)=-1[/tex] for coterminal angles [tex]$\frac{3\pi }{2}+2\pi n$[/tex]
Once we just want the interval [tex][0, 2\pi)[/tex]
The solution is [tex]$\frac{3\pi }{2}$[/tex]
A quadrilateral has vertices at $(0,1)$, $(3,4)$, $(4,3)$ and $(3,0)$. Its perimeter can be expressed in the form $a\sqrt2+b\sqrt{10}$ with $a$ and $b$ integers. What is the sum of $a$ and $b$?
Answer:
a + b = 12
Step-by-step explanation:
Given
Quadrilateral;
Vertices of (0,1), (3,4) (4,3) and (3,0)
[tex]Perimeter = a\sqrt{2} + b\sqrt{10}[/tex]
Required
[tex]a + b[/tex]
Let the vertices be represented with A,B,C,D such as
A = (0,1); B = (3,4); C = (4,3) and D = (3,0)
To calculate the actual perimeter, we need to first calculate the distance between the points;
Such that:
AB represents distance between point A and B
BC represents distance between point B and C
CD represents distance between point C and D
DA represents distance between point D and A
Calculating AB
Here, we consider A = (0,1); B = (3,4);
Distance is calculated as;
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex](x_1,y_1) = A(0,1)[/tex]
[tex](x_2,y_2) = B(3,4)[/tex]
Substitute these values in the formula above
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}[/tex]
[tex]AB = \sqrt{( - 3)^2 + (-3)^2}[/tex]
[tex]AB = \sqrt{9+ 9}[/tex]
[tex]AB = \sqrt{18}[/tex]
[tex]AB = \sqrt{9*2}[/tex]
[tex]AB = \sqrt{9}*\sqrt{2}[/tex]
[tex]AB = 3\sqrt{2}[/tex]
Calculating BC
Here, we consider B = (3,4); C = (4,3)
Here,
[tex](x_1,y_1) = B (3,4)[/tex]
[tex](x_2,y_2) = C(4,3)[/tex]
Substitute these values in the formula above
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}[/tex]
[tex]BC = \sqrt{(-1)^2 + (1)^2}[/tex]
[tex]BC = \sqrt{1 + 1}[/tex]
[tex]BC = \sqrt{2}[/tex]
Calculating CD
Here, we consider C = (4,3); D = (3,0)
Here,
[tex](x_1,y_1) = C(4,3)[/tex]
[tex](x_2,y_2) = D (3,0)[/tex]
Substitute these values in the formula above
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}[/tex]
[tex]CD = \sqrt{(1)^2 + (3)^2}[/tex]
[tex]CD = \sqrt{1 + 9}[/tex]
[tex]CD = \sqrt{10}[/tex]
Lastly;
Calculating DA
Here, we consider C = (4,3); D = (3,0)
Here,
[tex](x_1,y_1) = D (3,0)[/tex]
[tex](x_2,y_2) = A (0,1)[/tex]
Substitute these values in the formula above
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}[/tex]
[tex]DA = \sqrt{(3)^2 + (- 1)^2}[/tex]
[tex]DA = \sqrt{9 + 1}[/tex]
[tex]DA = \sqrt{10}[/tex]
The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral
[tex]Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}[/tex]
[tex]Perimeter = 4\sqrt{2} + 2\sqrt{10}[/tex]
Recall that
[tex]Perimeter = a\sqrt{2} + b\sqrt{10}[/tex]
This implies that
[tex]a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}[/tex]
By comparison
[tex]a\sqrt{2} = 4\sqrt{2}[/tex]
Divide both sides by [tex]\sqrt{2}[/tex]
[tex]a = 4[/tex]
By comparison
[tex]b\sqrt{10} = 2\sqrt{10}[/tex]
Divide both sides by [tex]\sqrt{10}[/tex]
[tex]b = 2[/tex]
Hence,
a + b = 2 + 10
a + b = 12
Answer:
a+b=6
Step-by-step explanation:
The tutor verified answer is mostly correct however, if you look under both by comperision sections you will see that it is:
[tex]4\sqrt{2}[/tex] and [tex]2\sqrt{10}[/tex] thus the answer is 4+2=6
In the circle below, O is the center and mĞ= 128° What is the measure of angle HIG?
Answer:
HIG=28°
Step-by-step explanation:
HI is a diameter therefore it's measure is 180°
HI-IG=HG
180-128=HG
52°=HG
HIG=1/2HG
HIG=1/2(56°)
HIG=28°
plssssss help number 18 and 20
Answer:
18).Total mass of materials = 4.8kg
For gravel
55% of the materials are gravel
So we have
55/100 × 4.8 kg
= 2.64kg
For sand
30% of the materials are sand
We have
30/100 × 4.8
= 1.44kg
For cement
The remaining materials were cement so we add the masses of both the sand and gravel and subtract it from the total mass
That's
4.8 - (2.64 + 1.44)
4.8 - 4.08
= 0.72 kg
20).She earns £ 800 per week
She receives a raise of 7.5% which is
100 + 7.5 = 107.5%
So we have
107.5 / 100 × £ 800
= £ 860
She now earns £ 860 per week
Hope this helps you
Step-by-step explanation:
1)of 4.8kg concrete 55% is gravel,30% is sand and 15% is cement.
percent=Rate*Base
Pgravel=55%*4.8kg
Pgravel=2.64kg
Psand=30%*4.8kg
Psand=1.44kg
Pcement=15%*4.8kg
Pcement=0.72kg
2)percent=Rate*Base
percent=7.5%*£800
percent=60£
total earn=60£ + £800
total earn=£860