By respecting the given ratio:
1) 10 of blue paint and 15 of yellow.
2) 4 of blue paint and 6 of yellow.
3) 2 cans of blue paint and 3 of yellow.
On days 1 and 2 how much blue paint did Marc use? How much yellow paint?
We know that on day 1 he uses:
4 cans of blue paint.6 cans of yellow paint.On day 2 he uses:
6 cans of blue paint.9 cans of yellow:Adding that we get:
Cans of blue paint used: 4 + 6 = 10Cans of yellow paint used: 6 + 9 = 15How many cans has he left on day 3?He initially has 20 cans of yellow, so he has left:
20 - 15 = 5 cans of yellow.
He initially has 14 cans of blue, so now he has:
14 - 10 = 4
4 cans of blue paint.
3) How many cans should he use?
The original ratio is:
6 yellow to 4 blue.
The quotient gives: 6/4 = 3/2
So if she has 5 cans of yellow paint and 4 cans of blue paint, the maximum amount that he can use that respects that ratio is 3 cans of yellow paint and 2 cans of blue paint.
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answer the question with a reason, please
Answer:
Diagram A
Step-by-step explanation:
a line of best fit can only be drawn if thier is strong negative or positive correlation
help math thx!!! dont haft to explain
Answer:
Step-by-step explanation:
try number 1
From the value found for the x, the angle ABD is 37° and the angle DBC is 58°.
Linear Expression
A linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.
The question gives that the angle ABC is 95°. The angle ABC is composed of the angles ABD and DBC. Thus, you should sum the angles ABD and DBC, for finding x.
2x+23+9x-5=95
11x+18=95
11x=95-18
11x=77
x=7
Like x=7, you can find the angles ABD and DBC
Angle ABD = 2*7+23=14+23=37°Angle DBC = 9*7-5=63-5=58°Learn more about the algebraic expression here:
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Find the inverse of each function. Is the inverse a function? f(x)=x⁷
The inverse of the function x^7 is x^-7 and it is also a function.
An inverse function or an anti function is defined as a function, which can reverse into another function.
A standard method to find inverse of a function is to set y=f(x)
let y= f(x)=x^7
thus
[tex]\sqrt[7]{y}[/tex]=x
thus [tex]f^{-1}[/tex](y)=[tex]\sqrt[7]{y}[/tex]
thus [tex]f^{-1} (x)=\sqrt[7]{x}[/tex]
(To verify this if a function is inverse or not we are required to check for the identity)
f([tex]f^{-1}[/tex](x))=[tex]f^{-1}[/tex](f(x))=x
Therefore, The inverse of the function x^7 is x^-7 and it is also a function.
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solve for x.
60°
8x-4
Answer: x=8
Step-by-step explanation: i did this exact question on OW
What is the product 2 x-8 / x²-16 . x²+5 x+4 / x²+8 x+16 in simplest form? State any restrictions on the variable.
The required simplification of an expression is 2(x + 1) / (x + 4)(x + 4).
What is an expression?
An expression is any statement in mathematics written using numbers, variables and at least one operation present.
Simplification of the expression: 2x - 8 / x² - 16 . x² + 5x + 4 / x² + 8x + 16
Given an expression,
2x - 8 / x² - 16 . x² + 5x + 4 / x² + 8x + 16
On simplifying, we get,
(2x - 8).(x² + 5x + 4) / (x² - 16).(x² + 8x + 16)
For the numerator, (2x - 8).(x² + 5x + 4), we have,
= 2(x + 1)(x - 4)(x + 4)
For the denominator, (x² - 16).(x² + 8x + 16)
= (x + 4)(x - 4)(x + 4)(x + 4)
Now, (2x - 8).(x² + 5x + 4) / (x² - 16).(x² + 8x + 16)
= 2(x + 1)(x - 4)(x + 4) / (x + 4)(x - 4)(x + 4)(x + 4)
= 2(x + 1) / (x + 4)(x + 4)
The restriction to the given expression is that the denominator, x + 4 should not be 0.
Hence, the required simplification of an expression is 2(x + 1) / (x + 4)(x + 4).
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please help me solve 4 +6.5x< 36.5
The solution to the given inequality in inequality and interval notation form are x < 5 and ( -∞,5 ) respectively.
What is the solution to the given inequality?Given the inequality in the question;
4 + 6.5x < 36.5
First, move all terms not containing x to the right side of the inequality.
4 + 6.5x < 36.5
6.5x < 36.5 - 4
Subtract 4 from 36.5
6.5x < 36.5 - 4
6.5x < 32.5
Divide both sides by the coefficient of x
6.5x < 32.5
6.5x/6.5 < 32.5/6.5
x < 32.5/6.5
x < 5
The solution in inequality form is x < 5
The solution in interval notation is ( -∞,5 ).
Therefore, the solution to the given inequality in inequality and interval notation form are x < 5 and ( -∞,5 ) respectively.
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Answer:
X < 5
Step-by-step explanation:
The solution is so subtract the 4 with the 4 and 36.5 you cross out the 4 and subtract 4 form 36.5 which leaves you with 32.5. Then to get the variable by itself you divide 6.5 on both sides, then cross out the 6.5 and divide 6.5 on 32.5 which gives you 5. (I solved it by myself)
How would this word problem be solved?
A phone call costs $0.58 per minute for the first three minutes and $0.15 per minute for each additional minute. If the total charge for the call was $4.29, how many minutes long was the call?
Answer:
31 minutes in total
Step-by-step explanation:
Going step by step, where m = minutes after the first 3:
0.58 + 0.15m = 4.78
We want to solve for m, so we need to isolate it. The first step is to get rid of 0.58 to simplify our equation.
0.15m = 4.78 - 0.58
Now we have:
0.15m = 4.20
To isolate further, we need to remove 0.15.
m = 4.20 / 0.15
m = 28
Now, we add the first 3 minutes to m to get our total time.
28 + 3 = 31
-9x-9+5^3x4^4 I need step by step pleas
Answer:
32081.
Step-by-step explanation:
-9x-9+5^3x4^4
Using PEMDAS, the exponents are calculated first:
= -9 x -9 + 125 x 256
Next the multiplications:
= 81 + 32000
= 32081.
What is the slope of the line that passes
through the points (8, 2) and (10, 2)?
Write your answer in simplest form.
Answer:
Submit Answer
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attempt 1 out of a
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (8, 2 ) and (x₂, y₂ ) = (10, 2 )
m = [tex]\frac{2-2}{10-8}[/tex] = [tex]\frac{0}{2}[/tex] = 0
There are 3 consecutive integers. Four times the smallest integer is equal to six more than more than three times the largest. What is the smallest of the 3 integers?
Answer:
The answer is 12.
Step-by-step explanation:
Let the smallest number = x and the largest number = x+2(since the three numbers are consecutive, we would have to use x+2. If we wanted the second largest number, it would be x+1)
We would write the statement "four times the smallest integer is equal to six more than more than three times the largest" as:
4x = 3(x+2) + 6
Now just solve.
4x = 3x+6+6 distributive property
4x = 3x+12 simplify
x = 12 subtraction property
And since x is the smallest number, we have our answer.
Therefore, the answer is 12.
help me please just answer the question.
Answer:
the answer is A
Answer:
Step-by-step explanation:
b is the aswswer
Solve each equation. Check your answers. e³x=12
The value of the given equation is x = ln(4) / 3 ≈ 0.4621
property of logarithms:The features of log are employed to expand (or compress) a single logarithm into numerous logarithms. A logarithm is simply another way to express exponents. Thus, logarithmic features are derived from exponentiation qualities.
Solving for the equation:e³x=12
Can be written as:
[e^x] [e^(2x)] = 4
Using the property of power multiplication utilizing the same base
e ^ (x + 2x) = 4
e ^ (3x) = 4
Applying logarithm properties both side:
3x = ln(4)
ln(4) / 3 ≈ 1.38629 / 3 ≈ 0.4621
The value of the given equation is x = ln(4) / 3 ≈ 0.4621
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$10,000, time to double is 12 years, what is the annual rate & amount after 10 years?
well, double of 10000 is 20000, so hmmm happens in 12 years, ok
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$20000\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}[/tex]
[tex]20000=10000\left(1+\frac{~~ \frac{r }{100 } ~~}{1}\right)^{1\cdot 12} \implies \cfrac{20000}{10000}=\left( 1+\cfrac{r}{100} \right)^{12} \\\\\\ 2=\left( \cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{2}=\cfrac{100+r}{100}\implies 100\sqrt[12]{2}=100+r \\\\\\ 100\sqrt[12]{2}-100=r\implies {\LARGE \begin{array}{llll} \stackrel{\%}{5.95}\approx r \end{array}}[/tex]
now, what will it be after 10 years assuming we use 5.95%? mind you that's a rounded figure, but close enough.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to 5.95\%\to \frac{5.95}{100}\dotfill &0.0595\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A=10000\left(1+\frac{0.0595}{1}\right)^{1\cdot 10} \implies {\LARGE \begin{array}{llll} A \approx 17824.18 \end{array}}[/tex]
If mWVY = 70, find mYVX.
Answer:
Can I see a diagram?
Step-by-step explanation:
Expand each logarithm.
log√2x/y
Using logarithmic quotient rule, we expand each logarithm function log√2x/y as 1/2 log (2x) - log (y).
According to the question, we need to expand we expand logarithm function log√2x/y .In Logarithms, the power is raised to some numbers (usually, base number) to get some other number. It is an inverse function of exponential function.
Quotient rule for logarithm: log (a/b) = log (a) - log(b).
⇒ log√2x/y
Applying quotient rule to the above logarithm function, we get
log√2x/y = log (√2x) - log (y)
= log (2x)^1/2 - log (y) →(1)
Power rule for logarithm: log (a)ˣ = x log (a)
Applying power rule to the equation (1), we get
log (2x)^1/2 - log (y) = 1/2 log (2x) - log (y)
Hence, using logarithmic quotient rule, we expand each logarithm function log√2x/y as 1/2 log (2x) - log (y).
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Help please asap anyone
Answer:
x= 0 (B)
Step-by-step explanation:
hope this helps
Write the equation of a line perpendicular to 6x-7y=-4 that passes through the point (-6,5).
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]6x-7y=-4\implies 6x=7y-4\implies 6x+4=7y \\\\\\ \cfrac{6x+4}{7}=y\implies \qquad \stackrel{\stackrel{m}{\downarrow }}{\cfrac{6}{7}} x+\cfrac{4}{7}=y\qquad \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]
now, since we know that slope, let's check for a perpendicular line to it
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{6}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{6}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{6}}}[/tex]
so we're really looking for the equation of aline whose slope is -7/6 and that it passes through (-6 , 5)
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{6} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- \cfrac{7}{6}}(x-\stackrel{x_1}{(-6)}) \implies y -5= -\cfrac{7}{6} (x +6) \\\\\\ y-5=-\cfrac{7}{6}x-7\implies {\LARGE \begin{array}{llll} y=-\cfrac{7}{6}x-2 \end{array}}[/tex]
Answer:
Please read and try to understand it :>
Step-by-step explanation:
[tex]6x-7y=-4[/tex] is not the standard format for a straight line so you have to rearrange it:
[tex]y=\frac{6}{7} x +\frac{4}{7}[/tex]
To find the equation of a perpendicular line to the given equation, you have to first find the negative reciprocal of the gradient:
[tex]-\frac{7}{6}[/tex]
Since you want to find the equation of a perpendicular line that passes a certain point, you have to substitute the coordinates to the equation to find the y-intercept:
[tex]5=-\frac{7}{6} (-6)+c[/tex]
Solving:
[tex]5=-\frac{7}{6} (-6) +c\\ \\ 5=\frac{42}{6} +c\\ \\-\frac{42}{6} +5=c\\ \\-7+5=c\\\\ -2=c[/tex]
Final equation: [tex]y=-\frac{7}{6} x -2[/tex]
Write each expression as a single natural logarithm. ln 3-5 ln 3
Expression as a single natural logarithm is 0.01234567901.
What is natural logarithm?Given in the question an expression
ln 3 + 5 ln 3
ln 3 + ln [tex]3^{5}[/tex]
Apply multiplication rule
ln (3/[tex]3^{5}[/tex])
[tex]3^{5}[/tex] = 243
so
expression as a single natural logarithm is 0.01234567901.
The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.
The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).
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please help with this
Answer: i got no clue
Step-by-step explanation:
Find the inverse of each function. Is the inverse a function?
y=3 x+1
In mathematics, an inverse function is one that "reverses" another function. The inverse of each function y = 3x + 1 is y = x−13.
What is meant by inverse function?The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f is bijective.
An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.
Let the function be y = 3x+1
Replacing f(x) with y, we get
y = 3x+1
simplifying the above equation, we get
x = 3y + 1
Subtracting 1 from both sides to get
3y = x − 1
Dividing both sides by 3, we get
y = x−13
Replace y with f⁻¹(x), we get
f⁻¹(x) = x−13
The inverse of each function y = 3x+1 is f⁻¹(x) = x−13.
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What does this simplify to? -
-4(3-x) - 7x
Answer:
Step-by-step explanation:-12+4x-7x=12-3x.
UR MOM IS GONNA BE SO PROUD OF YOU!!!!!!!!!!!!!
Complete the missing angles:Two angles of a quadrilateral are 110 and 50 and the other two angles are equal
Answer:
100
Step-by-step explanation:
a quadrilateral has a total of 4 angles
so the sum of all four angles is 360degre
so let the two equal angles be 2x
so 110+50+2x=360
2x=360-160
2x=200
x=200/2
therefore x = 100
A certain star is 4.6 x 10^2 light years from the Earth. One light year is about 5.9 x 10^12 miles. How far from the earth (in miles) is the star? Has to be answered in scientific notation
The distance of the earth from the star is mathematically given as
2.537 x 10¹⁵ miles
How far from the earth (in miles) is the star?Generally, the Coefficients for the problem are mathematically given a
Coefficients =4.6 x 5.9
Coefficients =27.14
For Exponents
Exponents 10² x 10¹² = 10⁽²⁺¹²⁾
Exponents =10¹⁴
In conclusion, After that, we put them together once again to produce a scientific notation:
25.37 x 10¹⁴
2.537 x 10¹⁵ miles
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Write each expression as a single logarithm. Identify any properties used. log x-log y
log x-log y = log ( x/y) we use this properties Quotient in the equation.
A logarithm is defined simply?
The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2: log 100 = 2.How does exponential growth utilise e?
e is the constant growth rate that all processes that are growing continuously share. With e, you may compare a simple growth rate—where all change occurs at the end of the year—with a compound, continuous growth rate, where growth occurs once per nanosecond or quicker.You use this properties Quotient in the equation -
log x-log y = log ( x/y)
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When thinking about the small group as a system, what is the key component that connects all of the system's relevant parts?
a. equifinality
b. summativity
c. multifinality
d. communication
e. minifinality
When thinking about the small group as a system, the key component that connects all of the system's relevant parts is D. Communication.
How to illustrate the information?It should be noted that the system framework is important as it reminds us that the piece of puzzle interacts with each other.
Therefore, when thinking about the small group as a system, the key component that connects all of the system's relevant parts is communication.
The sender, also known as the communicator or source, is where communication starts. The sender wishes to share some kind of information with the recipient(s), such as a request, query, or idea.
Understanding comes through good communication. Four essential elements make up the communication process. These elements consist of encoding, transmission medium, decoding, and feedback.
It should be noted that communication links the parts together.
Therefore when thinking about the small group as a system, the key component that connects all of the system's relevant parts is Communication.
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a box in a certain supply room contains four 40-w light bulbs, five 60-w light bulbs, and six 75-w light bulbs. suppose that three bulbs are randomly selected. (a) what is the probability that exactly two of the selected bulbs are rated 75-w? (b) what is the probability that one bulb of each type is selected? (c) what is the probability that all three of the selected bulbs have the same rating?
The probability that exactly two of selected are 75W is 0.2967 , probability that exactly two of the selected bulbs are rated 75W is 0.2637 , probability that one bulb of each type is selected is 0.0747 .
Probability of an event E denoted by P(E) is defined as number of favorable outcomes divided by total number of outcomes.
In the given question
40W bulbs = 4
60W bulbs = 5
75W bulbs = 6
Total number of bulbs = 4+5+6=15.
Part(a)
probability that exactly two of the selected bulbs are rated 75-w
Selection of 3 bulbs from 15 bulbs can be done in C(15,3) ways.
[tex]=\frac{15!}{3!*12!}[/tex]
[tex]=\frac{15*14*13*12!}{12!*3!} \\ \\ =\frac{15*14*13}{3*2*1}[/tex]
=455 ways
Total number of ways = 455 ...(i)
Now,
Number of ways of selecting 2 ,75W bulbs and 1 bulb from the remaining is C(6,2)*C(9,1).
= C(6,2)*C(9,1)
[tex]=\frac{6!}{2!*4!} *\frac{9!}{1!*8!} \\ \\ =\frac{6*5*4!}{2*4!} *\frac{9*8!}{8!}[/tex]
[tex]=\frac{6*5}{2} *9\\ \\ =15*9\\ \\ =135[/tex]
the probability that exactly two selected bulbs are rated 75W = 135/455 =0.2967
Part(b)
probability that one bulb of each type is selected .
Number of ways of selecting one bulb from each type = selecting 1 bulb from four 40W bulbs + 1 bulb from 60W bulbs + 1 bulb from 75W bulbs.
Number of ways of selecting one bulb from each type=C(4,1)*C(5,1)*C(6,1)
[tex]=C(4,1)*C(5,1)*C(6,1)\\ \\ =\frac{4!}{3!*1!} *\frac{5!}{4!*1!} *\frac{6!}{5!*1!}[/tex]
[tex]=\frac{4*3!}{3!} *\frac{5*4!}{4!} *\frac{6*5!}{5!}[/tex] ...( as 1!=1)
[tex]=4*5*6\\ \\ =120[/tex]
Number of ways of selecting one bulb from each type = 120
Total number of ways = 455 ...from equation (i)
Probability that exactly two bulbs selected are rated 75W =120/455
=0.2637
Part(c)
probability that all three of the selected bulbs have the same rating
Number of ways three bulbs of same rating are selected = (all 3 from 40W bulbs )+(all 3 are from 60W bulbs )+( all 3 are from 75 W bulbs)
[tex]=C(4,3)+C(5,3)+C(6,3)[/tex]
[tex]=\frac{4!}{1!*3!} +\frac{5!}{2!*3!} +\frac{6!}{3!*3!} \\ \\ =\frac{4*3!}{3!} +\frac{5*4*3!}{2!*3!} +\frac{6*5*4*3!}{3*2*3!}[/tex]...( as1!=1)
[tex]=4+10+20[/tex]
[tex]=34[/tex]
Number of ways three bulbs of same rating are selected = 34
Total number of ways = 455 ...from equation (i)
Probability that all three of the selected bulbs have the same rating=34/455 = 0.0747
Therefore ,(a) the probability that exactly two of selected are 75W is 0.2967 , (b) probability that exactly two of the selected bulbs are rated 75W is 0.2637 (c) probability that one bulb of each type is selected is 0.0747 .
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David travelled 4/5 of his trip by bicycle and the rest of the distance by foot. if the whole trip was 160 km, how many kilometers did he travel by foot?
David travelled 32 kilometres of the entire trip by foot
How to calculate the distance David travelled by foot ?David travelled 4/5 of his trip by bicycle and the rese was done by foot
The whole trip was 160 km
The first step is to calculate the distance travelled with the bicycle
4/5 × 160
= 128
Therefore the distance travelled by foot can be calculated as follows
= 160-128
= 32
Hence David travelled 32km by foot
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Answer:32
Step-by-step explanation:32
can you help solve the problem
Answer: D
Explained: you find the solutions to x and the y axis to graph
Each pair of values is from a direct variation. Find the missing value. (3,7),(8, y)
The missing value of direct variation is 56/3
What is direct variation ?The direct variation property states that , whenever the division of values of two quantities is a constant value then there is same variation between these two corresponding values. Or we can also say that if the divisible nature of two corresponding values is constant, then one quantity is directly varies with second quantity. That mean if one quantity increase other will also increase and vice versa.
Let say if x and y are two values and k is a constant value, then
According to direct variation
k = y/x or y = k x
In the given question,
Take the order pair (3,7)
As it is an direct variation, we can substitute it
y=k x
7=k (3)
K=7 / 3
Now find the direct variation equation
y=k x
Also, k=7/3
Solve this equation for the second pair (8,y)
As, y=7/3 x
y= 7/3 (8) = 56/3
Therefore, missing value is 56/3
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Find the surface area of D
Answer:
151 cm² (i don't know what unit you were given so im going to use cm)
Step-by-step explanation:
Part One: finding the missing side (h)
h = a² = b² + c²
13² = 12² + c²
169 = 144 + c²
169 - 145 = c²
= 25
square root of 25 = c
5 = c
area of top triangular area = ½ b × h
= ½ × 12 × 5
= 30 cm²
Part Two
area of rectangle = l × b
= 12 × 8
= 96 cm²
Part Three
area of square = l × l
= 5 × 5
= 25 cm²
total surface area = (30 + 96 + 25) cm²
= 151 cm²