No extraneous solution to the equation
The equation is
2[tex](x - 1)^{4/1}[/tex] + 4 = 36
We have to find the extraneous solution of the equation and for this first, we need to find the value of x.
2[tex](x - 1)^{4}[/tex] + 4 = 36
2[tex](x - 1)^{4}[/tex] = 32
[tex](x - 1)^{4}[/tex] = 16
x - 1= 2
x = 3
Now we will put the value of x in the equation.
2[tex](3 - 1)^{4}[/tex] + 4 = 36
2 [tex]2^{4}[/tex] + 4 = 36
2 × 16 + 4 = 36
32 + 4 = 36
36 = 36
Therefore we get that there is no extraneous solution to the equation, x = 3 is the solution of the equation.
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(Equivalent Algebraic Expressions LC)
Simplify this please!!!
Answer: X^3 / Y^5
The first answer choice
Step-by-step explanation:
Use the interactive to graph a line with a slope of zero and passing through the point (0,4).
Which statements are true for the graph? Check all that apply.
The line is horizontal.
The line is vertical.
The line goes through (0,0).
The line goes through (4,4).
The x-values are all 0.
The y-values are all 4.
Answer:
THE CORRECT ANSWER'S ARE A,D AND F
Step-by-step explanation:
did the test on edge .
A:B = 6:7 and A=30. Find B.
Please help me out with this, i dont know how to work it out, thank you.
Step-by-step explanation:
it is a ratio, and as such it is simply a fraction.
we can also write it
A/B = 6/7
and it gives us the same information.
and so,
30/B = 6/7
30 = 6B/7
210 = 6B
B = 210/6 = 35
x^2 + 9x + 14 = ( x+_)(x+_)
quickly!!!
Answer:
[tex](x+7)(x+2)[/tex]
Step-by-step explanation:
We have the equation:
[tex]x^{2} +9x+14[/tex].
The factors of 14 are 1, 2, 7 and 14.
Now, all we have to do is find two numbers that add up to 9.
We see that 2 and 7 add up to 9.
Therefore,
[tex]x^2+9x+14=(x+7)(x+2)[/tex]
Hope this helped! Have a great day!
Answer:
(x+7)(x+2)
Step-by-step explanation:
x^2+2x+7x+14 (Because 7 and 2 add to give 9 and multiply to give 14)
x(x+2) +7(x+2) (Take out common factors, factorising)
(x+2)(x+7) (Put the things common in a bracket together and the bits that are outside in another bracket)
4. Use the equations below to find the indicated values.
a. f(x) = 6x +5
i) f(2)=
b. g(x) = 3x
i) g(4) =
ii) f(-2) =
ii) g(0) =
iii) f(1/2) =
iii) g(-4)=
Answer:
f(2) = 17g(4) = 12f(-2) = -7g(0) = 0f(1/2) = 8g(-4) = -12Step-by-step explanation:
We have
[tex]f(x) = 6x + 5[/tex]
[tex]g(x) = 3x[/tex]
To find the value of either of these functions for a specific value of x, simply substitute that value into the corresponding function equation.
[tex]\bold{f(2)}[/tex]
Substitute x with 2 in 6x + 5
==> [tex]6\cdot \:2+5=17[/tex] (Answer)
[tex]\bold{g(4)}[/tex]
Substitute x with 4 in g(x) = 3x
==> [tex]3 \cdot4=12[/tex] (Answer)
[tex]\bold{f(-2)}[/tex]
Substitute x with -2 in 6x + 5
[tex]6\left(-2\right)+5=-7[/tex] (Answer)
[tex]\bold{g(0)}[/tex]
Substitute x with 0 in g(x) = 3x
==> [tex]3\cdot0=0[/tex] (Answer)
[tex]\bold{f(\frac{1}{2})}[/tex]
Substitute x with [tex]\frac{1}{2}[/tex] in 6x + 5
==> [tex]6\cdot \frac{1}{2}+5 = 3 + 5 = 8[/tex] (Answer)
[tex]\bold{g(-4)}[/tex]
Substitute x with -4 in g(x) = 3x
==> [tex]3\left(-4\right) = -12[/tex] (Answer)
x + 2y3z = 25
3x - 3y + 4z = -23
-4x+y-z = -25
Values of x y z for system of equation are
x=[tex]\frac{565}{54}[/tex]
y=[tex]\frac{703}{54}[/tex]
z=[tex]\frac{-23}{6}[/tex]
we have system of equation as follows
x + 2y+3z = 25
z=(25-x-2y)/3..........(A)
3x - 3y + 4z = -23
z=(3y-3x-23)/4........(B)
-4x+y-z = -25
z=(25-4x+y)..............(C)
Equating we get
(25-x-2y)/3=(3y-3x-23)/4=(25-4x+y)
Solving this we get
x=[tex]\frac{565}{54}[/tex]
y=[tex]\frac{703}{54}[/tex]
z=[tex]\frac{-23}{6}[/tex]
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The following question has two parts. First, answer part A. Then, answer part B. Part A A high school athlete ran the 100 meter sprint in 13.245 seconds. Round the time to the nearest tenth. Enter the answer in the box. seconds Part B Explain how you arrived at the answer. Include any rules that you followed.
If the sprinter ran the race for 13.245 seconds, if we are to represent it in tenth then it would be written as 13.2
What is tenth in mathematics?This is the term that is used to refer to the place value that would come immediately after the decimal point that we have in a group of digits that are a decimal.
In the question, the rule I followed is the one that I have explained above. The number that is after the decimal value is given as 2.
Hence we can say that the the answer after it has been rounded to the nearest tenth is 13.2
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The mass of a bar of chocolate is 1800g
The density of the chocolate is 9g/cm
Find the mass of the ball in kg
The mass of the bar of chocolate in kilogram, kg is calculated to be 1.8kg
How to find the mass of the bar in kgGiven data
mass of a bar of chocolate is 1800g
density of the chocolate is 9g/cm
density is defined the ratio of mass and volume. therefore the density of the chocolate will be the ratio of the mass of the chocolate bar to the volume of the chocolate. this represented mathematically as:
The mass of the bar of chocolate is given in grams as 1800g
converting the unit to kg is done as follows
if 1kg is equal to 1000g, then how many kg is 1800g
= 1800 / 1000
= 1.8 kg
hence the mass of the chocolate bar in kg is 1.8 kg
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Find the domain, points of discontinuity, and x - and y - intercepts of each rational function. Determine whether the discontinuities are removable or non-removable. y=2x²+5 / x²-2 x
The domain of given points are :
IR x ≠ ± √2
Points of discontinuity - x = ± √2 ( non removable / asymptote )
x - intercept =± √-5/2 , y - intercept = 5/2
What is rational functions ?Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere. First example: f(x) = x/ (x - 3).
CALCULATIONy=2x²+5 / x²-2 x
= 2[tex]x^{2}[/tex]+5/(x-√2)(x+√2)
The domain of given points are :
IR x ≠ ± √2
Points of discontinuity - x = ± √2 ( non removable / asymptote)
x-intercept :
2√10x=2[tex]x^{2}[/tex]+5+2√10x
2[tex]x^{2}[/tex] = -5
[tex]x^{2}[/tex]=-5/2
x = ±√-5/2
y - intercept :
2 * [tex]0^{2}[/tex] + 5 / ( 0-√2)(0+√2)
= 5/2
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Rewrite in simplest rational exponent form
Show each step of your process.
The simplest rational exponent form is [tex]x^\frac{3}{4}[/tex] .
A rational exponent is defined as an exponent that can be expressed as p/q. where q ≠ 0. The common notation for rational exponents is x^m/n. where x is the base (a positive number) and m/n is a rational number.An exponential expression of the form am has a rational exponent if m is a rational number. Powers and roots of numbers are represented together in rational exponents.We have given a rational exponent [tex]\sqrt{x} .\sqrt[4]{x}[/tex] . ...(1)
By formula [tex]\sqrt[4]{x}[/tex] can be written as [tex]x^\frac{1}{4}[/tex] and [tex]\sqrt{x}[/tex] can be written as [tex]x^\frac{1}{2}[/tex] .
Put in equation (1) , we get
[tex]\sqrt{x} .\sqrt[4]{x}=x^\frac{1}{2} .x^\frac{1}{4} \\[/tex] ...(2)
Using formula [tex]a^\frac{m}{n} \times a^\frac{p}{q} = a^{\frac{m}{n} +\frac{p}{q} }[/tex]
Equation (2) can be written as
[tex]\sqrt{x} .\sqrt[4]{x}=x^{\frac{1}{2} +\frac{1}{4}}\\\\\sqrt{x} .\sqrt[4]{x}=x^{\frac{2+1}{4} }\\\\\sqrt{x} .\sqrt[4]{x}=x^{\frac{3}{4} }[/tex]
Hence , on simplification , we get [tex]x^\frac{3}{4}[/tex] .
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Find the average rate of change of g(x) = 3x³ + 1 from æ =
- 1 to x = 4.
The average rate of change or the slope is found as 39.
What is the definition of line slope/ average rate of change?A line's slope is a measure of its steepness and orientation. The slope of a line can be calculated using any 2 different points on that line.The slope of a line formula calculates the ratio of "vertical change" to "horizontal change" between two distinct points on a line.The net change in y coordinates is Δy, while the net change in x coordinates is Δx.The slope of the line is given by;
m = (y₂ - y₁)/(x₂ - x₁)
The function is given as;
g(x) = 3x³ + 1
The points are; -1 and 4.
Put x = -1
g(-1) = 3(-1)³ + 1
g(-1) = -2
Put x = 4
g(4) = 3(4)³ + 1
g(4) = 193
The points are;
(x₁ ,y₁) = (-1, -2)
(x₂, y₂) = (4, 193)
Put the values in the slope formula;
m = (193 + 2)/(4 + 1)
m = 195/5
m = 39
Thus, the value of the average rate of change is 39; which is also the slope of the function.
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How do I do this ???
Let f(x)=7 x+5 and g(x)=x². Perform each function operation and then find the domain of the result.
f/g(x)
The domain of the result f/g(x) is (7 /x ) + (5/x^2).
The two functions are:
f(x) = 7x + 5
and
g(x) = x^2
For calculating f/g(x)
f/g(x) is equivalent to f(x) / g(x)
Hence (f / g)(x) = f(x) / g(x)
= 7x + 5 / x^2
= (7 /x ) + (5/x^2)
the domain of the result f/g(x) is (7 /x ) + (5/x^2).
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What values of x and y satisfy the system of equations 10x=5y−8 15x=−5y−2?
[tex]\begin{array}{llll} 10x=5y-8\\\\ 15x=-5y-2\\\\ \end{array}\implies \stackrel{\textit{using elimination}}{\begin{array}{llll} 10x-5y=-8\\\\ 15x+5y=-2\\\cline{1-1} 25x+0=-10 \end{array}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]25x=-10\implies x=\cfrac{-10}{25}\implies x=-\cfrac{2}{5} \\\\\\ \stackrel{\textit{substituting "x" in the 1st equation}}{10\left(-\frac{2}{5} \right)=5y-8\implies }-4=5y-8\implies 4=5y\implies \cfrac{4}{5}=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\LARGE \begin{array}{llll} \left( -\frac{2}{5}~~,~~\frac{4}{5} \right) \end{array}}~\hfill[/tex]
Please help me understand this
2x+3=7x
Answer:
x = 3/5
Step-by-step explanation:
Isolate the x by subtracting 2x from both sides
2x + 3 = 7x
-2x -2x
3 = 5x, Then divide by 5 on both sides
x = 3/5
Answer:
[tex] \sf \large \: x = \frac{3}{5} [/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
2x+3=7x
Step 1: Subtract 7x from both sides.
2x+3−7x=7x−7x
−5x+3=0
Step 2: Subtract 3 from both sides.
−5x+3−3=0−3
−5x=−3
Step 3: Divide both sides by -5.
−5x/−5 = −3/−5
x=3/5
(the cube root of 125 − 14 ÷ 2)(3 − 5)2 step by step
Answer:
18
Step-by-step explanation:
[tex] \sf( \frac{ ∛125 \: - \: 14 }{2})(3 - 5)2[/tex]
Apply rule: ([tex] a[/tex]) = [tex] a[/tex]
[tex] \sf( \frac{ ∛125 \: - \: 14 }{2}) = \: \sf\frac{ ∛125 \: - \: 14 }{2}[/tex]
[tex] = \sf \frac{∛125 \: - \: 14 }{2}(3 - 5)2[/tex]
Substract the numbers (3-5) = (-2)
[tex] = \sf \frac{∛125 \: - \: 14 }{2}( - 2)2[/tex]
Change 2 to fraction: [tex] \sf \frac{2}{1} [/tex]
[tex] = \sf \frac{∛125 \: - \: 14 }{2} \times \frac{2}{1} ( - 2)[/tex]
Cross- cancel common factor 2
[tex] = \sf \frac{∛125 \: - \: 14 }{1} ( - 2)[/tex]
Let's calculate [tex] \sf \frac{∛125 \: - \: 14 }{1} [/tex]
[tex] = \sf \frac{∛125 \: - \: 14 }{1} [/tex]
Apply a fraction rule = a/1 = a
[tex] = \sf ∛125 \: - \: 14 [/tex]
[tex] \sf = - 9[/tex]
[tex] \sf \: = - 9( - 2)[/tex]
[tex] \sf \: = 18[/tex]
What’s the answer for number 8? Show work and explain
Answer:
so simple do it yourself and use the formula when is given in the text book to solve
An employee earns $15 an hour for the first 20 hours worked during the week. The employee earns an extra $5 per hour for every additional hour over 20 hours worke per week. The scenario is represented by the function f(x). How much does the employee earn by working 25 hours in one week?
The money that the employee earn by working 25 hours in one week is $400.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let f(x) represent the amount of money that the employee earn by working x hours. If the employee work more than 20 hours, then:
f(x) = 15x + 5(x - 20)
For 25 hours:
f(25) = 15(25) + 5(25 - 20) = 400
The money that the employee earn by working 25 hours in one week is $400.
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Solve for x
−6−(−4x+2)−x=-(5x-2)
Answer: x=5/4
Step-by-step explanation:
−6−(−4x+2)−x=-(5x-2)
−6+4x-2−x=-5x+2
-x+4x-6-2=-5x+2
3x-8=-5x+2
3x-8+8=-5x+2+8
3x=-5x+10
3x+5x=-5x+5x+10
8x=10
x=10/8
x=5/4
Hi there,
I hope you and your family are staying safe and healthy during this anomalous time.
[tex]-6 -(-4x + 2) - x = -(5x-2)[/tex]
The first step is to distribute
[tex]-6 + 4x - 2-x=-(5x-2)[/tex]
Now let's subtract the numbers
[tex]-8 +3x = -(5x-2)[/tex]
[tex]3x - 8 = -(5x-2)[/tex]
[tex]3x - 8 = -5x+2[/tex]
[tex]3x = -5x + 2 +8\\3x = -5x +10[/tex]
[tex]3x + 5x = 10 \\8x = 10\\x = \frac{10}{8}[/tex]
Once we simplify that, we get:
[tex]x = \frac{5}{4}[/tex] as the answer
Happy to help! All the best this semester.
Use breaking apart to complete the calculation. 4 X 23 =
Using breaking apart technique 4 X 23 = 92
What does the multiplication breaking apart technique entail?To make the multiplication process simpler, you split up one or more of the numbers. It also explains why you would "carry" a number to the following column.
What does it mean to disintegrate?split apart definitions. verb: break anything down into its component parts. substitute words: separate, dismantle, take apart
According to the given question
4×23 = (20×4)+(3×4)
=80+12
=92
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Rational Or Irrational? PLEASE hurry!!!
Answer:
-1.7 = rational
1.083 = rational
1.22345721 = rational
-1.090909 = rational
Step-by-step explanation:
Izzy runs on the school track team. She runs 4 miles in hour.
3
What is Izzy's speed in miles per hour?
Izzy's speed in miles per hour is ?
10
69
9
10
3
1
15
9
10
Answer: Izzy's speed is [tex]6\frac{9}{10}[/tex] mph.
Step-by-step explanation: You have to divide the number of miles by the number of hours.
[tex]4\frac{3}{5} / \frac{2}{3}\\[/tex]
Convert the mixed fraction [tex]4\frac{3}{5}[/tex] to an improper fraction.
[tex]\frac{4 * 5 + 3}{5} / \frac{2}{3} = \frac{23}{5} / \frac{2}{3}[/tex]
Multiply the first fraction by the reciprocal of the second fraction (the second fraction upside down).
[tex]\frac{23}{5} / \frac{2}{3} = \frac{23}{5} * \frac{3}{2} = \frac{23 * 3}{5*2} = \frac{69}{10}[/tex]
Convert the result into a mixed fraction.
69 / 10 = 6 with a remainder of 9
A: [tex]6\frac{9}{10}[/tex]
Please help me find the value of x.
[tex]\huge\boxed{\sqrt5}[/tex]
To find the value of [tex]x[/tex], we'll use the Pythagorean theorem.
The following formula applies, with the lengths of the sides with the right angle being [tex]a[/tex] and [tex]b[/tex], and the hypotenuse being [tex]c[/tex]:
[tex]a^2+b^2=c^2[/tex]
Substitute the values in.
[tex]x^2+(\sqrt{11})^2=4^2[/tex]
Square the numbers as possible.
[tex]x^2+11=16[/tex]
Subtract 11 from both sides of the equation.
[tex]x^2=5[/tex]
Take the square root of both sides of the equation to solve for [tex]x[/tex].
[tex]x=\sqrt5[/tex]
An environmental equipment supplier sells hemispherical holding ponds for treatment of chemical waste. The volume of a pond is V₁=1/2(4/3 π r₁³) , where r₁ is the radius in feet. The supplier also sells cylindrical collecting tanks. A collecting tank fills completely and then drains completely to fill the empty pond. The volume of the tank is V₂=12 π r₂², where r₂ is the radius of the tank.
b. You want to double the radius of the pond. How will the radius of the tank change?
The radius of the tank should increase √ 2 times.
We are given that:
To fill a pond whose volume is given as V₁ = 1 / 2 (4 / 3 π r₁³), we need a cylindrical tank whose volume is given by V₂ = 12 π r₂².
This means that the volume of the pond should be equal to the volume of the cylinder.
So, we get that:
1 / 2 (4 / 3 π r₁³) = 12 π r₂².
4 / 3 π r₁³ = 24 π r₂²
r₁³ = 18 r₂²
r₂ = √ ( r₁³ / 18)
r₂ = r₁ / 3 √r₁ / 2
Now, we will double the radius of the pond.
So, r₁ will become 2 r₁
Substituting it, we get that:
R₂ = 2r₁ / 3 √2r₁ / 2
R₂ = 2r₁ / 3 √r₁
So, we can see that:
R₂ / r₂ = 2r₁ / 3 √r₁ / (r₁ / 3 √r₁ / 2)
R₂ / r₂ = 2 / √2 = √ 2
Therefore, the radius of the tank should increase √ 2 times.
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2. Use Structure Why do you multiply by a power
of 10 when writing a repeating decimal as a
rational number?
ext
Answer: Use Structure multiply by a power of 10 when writing a repeating decimal as a rational number is 1/5.
Step-by-step explanation:
Define Decimal number :
A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.
Example: the numbers we use in everyday life are decimal numbers, because they are based on 10 digits (0,1,2,3,4,5,6,7,8 and 9). "Decimal number" is often used to mean a number that uses a decimal point followed by digits that show a value smaller than one. Example: 45.6 (forty-five point six) is a decimal number.
Define Rational numbers :
Rational number, in arithmetic, a number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.
Example : a rational number is a type of real number, which is in the form of p/q where q is not equal to zero. Any fraction with non-zero denominators is a rational number. Some of the examples of rational numbers are 1/2, 1/5, 3/4, and so on.
So, Given data,
Use Structure Why do you multiply by a power of 10 when writing a repeating decimal as a rational number?
Then we can write,
Let us assume to multiply by some number (10, 100, 1000, etc.)
so that,
when we subtract the original number from the multiple, the repeating part cancels out.
If we multiply by 10.
we get 10x = 2
x = 2/10
x = 1/5
Therefore ,
x = 1/5 is Rational number.
So,
Use Structure multiply by a power of 10 when writing a repeating decimal as a rational number is 1/5.
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What is the value of the expression (-2 3/5)(-0.5)?
Answer:
1.3
Step-by-step explanation:
(−2 3/5)(−0.5)
=(−13/5)(−0.5)
=−13/5(−0.5)
=1.3
=1.3
Nick has $50 to spend during fall break. he decides to spend $10 each day. which equation represents the amount of money nick has left, y, and the number of days x?
Answer:
$50 = 5 days
$40 = 4 days
$30 = 3 days
$20 = 2 days
$10 = 1 day
Step-by-step explanation:
hope this helps = )
Someone help me outtt
Answer:
I THINK ITS B
Step-by-step explanation:
CORRECT ME IF I'M WRONG!!!
You have solved equations containing square roots by squaring each side. You were using the property that if a=b then (a²=b²). Show that the following statements are not true for all real numbers.
b. If a ≤ b then a²≤ b² .
If a ≤ b, then it is not true for all real numbers that a²≤ b² .
Consider a ≤ b.
Then squaring on both sides,
⇒ a²≤ b² .
But this is true only when both a and b are non-negative numbers.
For example, if we take a = 2 and b = 5, then clearly,
2² = 4 ≤ 5² = 25
Now we need to prove that this result is not true for all real numbers. So we find two real numbers a and b which does not follow this result.
Let a = -7 and b = 3
So here, a < b
Now a² = (-7)² = 49
and b² = 3² = 9
So here, a² > b².
Thus a = -7 and b = 3 is the required counter example to show that the given result is not true for all real numbers.
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A polygon has vertices A (5, -1), B (21, 11), C (26, -1), and D (2, -8).
Part A. What is the perimeter of ABCD to the nearest tenth of a unit?
Part B. What is the area of ABCD to the nearest tenth of a square unit?
Enter the correct answers in the boxes.
A. Perimeter: units
B. Area: square units
Check the picture below.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad B(\stackrel{x_2}{21}~,~\stackrel{y_2}{11}) ~\hfill AB=\sqrt{(~~ 21- 5~~)^2 + (~~ 11- (-1)~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 16 )^2 + ( 12)^2}\implies \boxed{AB=20}[/tex]
[tex]B(\stackrel{x_1}{21}~,~\stackrel{y_1}{11})\qquad C(\stackrel{x_2}{26}~,~\stackrel{y_2}{-1}) ~\hfill BC=\sqrt{(~~ 26- 21~~)^2 + (~~ -1- 11 ~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 5)^2 + ( -12)^2}\implies \boxed{BC=13} \\\\\\ C(\stackrel{x_1}{26}~,~\stackrel{y_1}{-1})\qquad D(\stackrel{x_2}{2}~,~\stackrel{y_2}{-8}) ~\hfill CD=\sqrt{(~~ 2- 26~~)^2 + (~~ -8- (-1)~~)^2} \\\\\\ ~\hfill CD=\sqrt{( -24)^2 + ( -7)^2}\implies \boxed{CD=25}[/tex]
[tex]D(\stackrel{x_1}{2}~,~\stackrel{y_1}{-8})\qquad A(\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) ~\hfill DA=\sqrt{(~~ 5- 2~~)^2 + (~~ -1- (-8)~~)^2} \\\\\\ ~\hfill DA=\sqrt{( 3)^2 + ( 7)^2}\implies \boxed{DA=\sqrt{58}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{20~~ + ~~13~~ + ~~25~~ + ~~\sqrt{58} ~~ \approx ~~ \text{\LARGE 65.6}}[/tex]
now, as far as the area goes, let's check the picture below, hmmm, there are two triangles, both have a base of 21, and you can see their heights there, well, let's simply get the area of each triangle and sum them up.
[tex]\cfrac{1}{2}(21)(12)~~ + ~~\cfrac{1}{2}(21)(7)\implies 126~~ + ~~73.5\implies \text{\LARGE 199.5}[/tex]