I really need help solving thisIt’s from my trig prep bookIt asks to answer (a) and (b)
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The sum in summation notation is:
[tex]\sum ^4_{r\mathop{=}0}(-1)^r(4Crx^{4-r}y^r)[/tex]The expansion is:
[tex]81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12}[/tex]Explanation:Given the expression:
[tex](3x^5-\frac{1}{9}x^3)^4[/tex]In summation notation, this can be written as:
[tex]\sum ^4_{r\mathop=0}(-1)^r(4Crx^{4-r}y^r)[/tex]The simplified terms of the expression is:
[tex]\begin{gathered} 4C0(3x^5)^{\mleft\{4-0\mright\}}(\frac{1}{9}y^3)^0-4C1(3x^5)^{\mleft\{4-1\mright\}}(\frac{1}{9}y^3)^1+4C2(3x^5)^{\mleft\{4-2\mright\}}(\frac{1}{9}y^3)^2-4C3(3x^5)^{\mleft\{4-3\mright\}}(\frac{1}{9}y^3)^3+4C4(3x^5)^{\mleft\{4-4\mright\}}(\frac{1}{9}y^3)^4 \\ \\ =(3x^5)^4-4(3x^5)^3(\frac{1}{9}y^3)+6(3x^5)^2(\frac{1}{9}y^3)^2-4(3x^5)^{}(\frac{1}{9}y^3)^3+(\frac{1}{9}y^3)^4 \\ \\ =81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12} \end{gathered}[/tex]Related Questions
Clarence is saving money to buy a skateboard that costs $97.50. He has $15.05 already saved and plans to save $5.50 each week from his allowance. He also earns $15.60 every two weeks for walking dogs. Suppose Clarence wants to spend some of the money from walking dogs on other things. To the nearest dollar, how much would he need to save from walking dogs each week in order to buy the skateboard 4 weeks earlier than if he just saves his allowance?
Please explain. Thanks!
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Answer:88
Step-by-step explanation:
creat an espression that includes the zero property of exponents the multiplication property of exponents and the power of a power property of exponents
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All in one, or one expression for each property?
a) Zero property
[tex]\text{ (x + y)}^0\text{ = 1}[/tex]b) Multiplication property
[tex]\text{ x}^2\cdot x^5=x^{2+5}=x^7[/tex]c) Power property
[tex]\text{ (x}^2)^3=x^{2\cdot3}=x^6[/tex]d) All in one (this is the expression)
[tex]\mleft\lbrace\text{(x}^0)(x^3)\mright\rbrace\text{ }(x^2)^5[/tex][tex]\text{ }\mleft\lbrace1(x^3\mright)\}(x^{10})[/tex]
If we have a system of two linear equations in two variables that has no solution, what would we see on the graph?
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Answer:
The graph will have two lines which will never intersect
What is the probability that a randomly chosen marble is red or small?
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We have the next formula
[tex]P\mleft(RorS\mright)=P\mleft(R\mright)+P\mleft(S\mright)-P\mleft(RandS\mright)[/tex]P(R)=0.7
P(S)=0.9
P(RandS)=0.6
The probability that randomly chosen marbñe is red or small is
[tex]\begin{gathered} \\ P(RorS)=0.7+0.9-0.6=1 \end{gathered}[/tex]The formula log in a natural logarithm can be written as?
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Solution:
Given the logarithmic expression:
[tex]\log_545[/tex]According to the change of base formula,
[tex]\log_BA=\frac{\ln A}{\ln\text{ B}}[/tex]Thus, expressing the logarithm expression in a natural logarithm,
[tex]\log_545=\frac{\ln45}{\ln5}[/tex]Hence, we have
[tex]\frac{\ln45}{\ln5}[/tex]What is the distance from 7 to 0? O A. 7, because 171 = 7 Jurid O B. 7, because 171 = 7 O c. 7, because |-71 = -7 O D. -7, because [7] = -7
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The distance from 7 to 0 is 7 because the absolute value of 7 is 7.
Correct Answer: A
For which equation will x=-2 make the equation true? Equation 1: 2.4x+ 2.6 = 17 Equation 2: 16 = -8(-6 - 2x) X - 4 Equation 3: 3 Equation 4: -6 = -5x - 3+ Óx
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We need to check each of the options to determine which equation is true
x = -2
equation1: 2.4x + 2.6 = 17
2.4(-2) + 2.6 = 17
-4.8 + 2.6 = 17
-2.2 = 17
equation2: 16 = -8(-6 - 2x)
16 = -8(-6 -2(-2))
16 = -8(-6+4)
16 = -8(-2)
16 = 16
equation 3: 3
how do I find the decimal value of the fraction 11/16?
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You divide 11 by 16, as follow:
0.6875
16 l 110
-96
140
-128
120
-112
80
-80
0
As you can notice, the result of the division is 0.6875 (here you have used the rules for the division of a number over a greater number, which results in a decimal)
What type of number is {-4}{2}
−4/2
start fraction, minus, 4, divided by, 2, end fraction?
Choose all answers that apply:
(Choice A)
Whole number
(Choice B)
Integer
(Choice C)
Rational
(Choice D)
Irrational
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Answer:
B and C
Step-by-step explanation:
Whole numbers are:
0, 1, 2, 3, 4, 5, 6...
The number we are looking at is -4/2, which is -2. Whole numbers aren't negative. So not choice A.
Integers are:
...-3, -2, -1, 0, 1, 2, 3...
Positives and negatives are included (just no fractions or decimals) So, -4/2 which is -2 IS an integer.
Rational numbers can be written like a ratio (like a fraction) So -4/2 totally IS a rational number.
Irrational numbers are decimal numbers that go on forever without repeating, like pi and sqrt2 and sqrt5. -4/2 is NOT irrational.
what is the domain and range of {(1,0), (2,0), (3,0) (4,0), (5,0)}
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We have the following:
The domain is the input values or the values of x and the range is the output values or the values of y
Therefore:
[tex]\begin{gathered} D=\mleft\lbrace{}1,2,3,4,5\mright\rbrace \\ R=\mleft\lbrace0\mright\rbrace \end{gathered}[/tex]What is the Y intercept of the graph below? A. (0,-2)B. (0,-4) C. (0, 2) D. (0,4)
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Recall that the y-intercept of a graph is the point where the graph intersects the y-axis.
From the given graph we get that the line intersects the y-axis at (0,2).
Answer: Option C.
Line / contains the points (-4, -1) and (1, 1) asshown below.432-10x-212-1P-2--3-Line m will be drawn perpendicular to line I andcontaining point P. Identify the coordinates ofanother point on line m.(-1, 4)O (1,3)(-2,-4)(5,3)
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Let's begin by listing out the information given to us:
Line m is perpendicular to line P
Line P: (x, y) = (-4, -1), (1, 1)
We will proceed to calculate for the slope of the line P (as shown below):
Slope (m) = Δy/Δx
Slope (m) = (1 - - 1)/(1 - - 4) = 2/5
Slope (m) = 2/5
The slope of a parallel line is the negative reciprocal of the slope of the line.
Line m: slope (m) = -1/(2/5) = -5/2
Line m: slope (m) = -5/2
We calculate for the equation of the line using the point-slope equation. We have
y - y1 = m(x - x1) ⇒
(x1, y1) = (1, 1)
y - 1 = 2/5 (x - 1) ⇒ y - 1 = 2/5x - 2/5
y = 2/5x - 2/5 + 1
y = 2/5x + 3/5
We will proceed to put the value of the new slope into the equation. We have:
y = -5/2x + b ; (x, y) = (1, 1) ⇒ 1 = -5/2(1) + b
⇒ b = 5/2
Substitute the value of b into the point-slope equation, and we obtain the equation of line m. We have:
y = -5/2x + 5/2
John sells plain cakes for $8 and decorated cakes for $12. On a particular day, John started with a total of 100 cakes, and sold all but 4. His sales that day totaled $800.He sold ___plain cakes and ____decorated cakes that day.
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INFORMATION:
We know that:
- John sells plain cakes for $8 and decorated cakes for $12.
- On a particular day, John started with a total of 100 cakes, and sold all but 4.
- His sales that day totaled $800.
And we must find the number of plain cakes and decorated cakes that he sold that day.
STEP BY STEP EXPLANATION:
To find them, we can represent the situation using a system of equations
[tex]\begin{cases}x+y={100-4...(1)} \\ 8x+12y={800...(2)}\end{cases}[/tex]Where, x represents the number of plain cakes that he sold and y represents the number of decorated cakes that he sold.
Now, we must solve the system:
1. We must multiply the equation (1) by -8
[tex]\begin{gathered} -8(x+y)=-8(100-4) \\ -8x-8y=-768...(3) \end{gathered}[/tex]2. We must add equations (2) and (3)
[tex]\begin{gathered} 8x+12y=800 \\ -8x-8y=-768 \\ ---------- \\ 0x+4y=32 \\ \text{ Simplifying, } \\ 4y=32...(4) \end{gathered}[/tex]3. We must solve equation (4) for y
[tex]\begin{gathered} 4y=32 \\ y=\frac{32}{4} \\ y=8 \end{gathered}[/tex]4. We must replace the value of y in equation (1) and then solve it for x
[tex]\begin{gathered} x+8=100-4 \\ x=100-4-8 \\ x=88 \end{gathered}[/tex]So, we found that x = 88 and y = 8.
Finally, John sold 88 plain cakes and 8 decorated cakes.
ANSWER:
He sold 88 plain cakes and 8 decorated cakes that day.
Write a quadratic equation in standard form with the given roots. a. Write a quadratic equation with a double root of -5.
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a quadratic function has any root when replacing that number the equation is equal to zero
so
[tex](x+5)(x+5)[/tex]now solve the multiplication
[tex]\begin{gathered} (x\times x)+(x\times5)+(5\times x)+(5\times5) \\ x^2+5x+5x+25 \\ x^2+10x+25 \end{gathered}[/tex]Susan has a job selling cars, and earns 1.25% commission on the first $100,000 in sales,The commission increases to 4.95% on the next $200,000. Last month her total sales were$387,000. How much was her commission if she received 7.25% for any sales over $300,000
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Solution:
Susan earns a commission based on car sales made.
Given:
Total sales made for the month = $387,000
Her commission is calculated based on levels and commision rate for each level.
On the first $100,000, she earns 1.25% commission.
Total sales at this level is $100,000
[tex]\begin{gathered} \text{Commision made on the first \$100,000 is;} \\ \frac{1.25}{100}\times100000=\text{ \$1,250} \\ =\text{ \$1,250} \end{gathered}[/tex]On the next $200,000, she earns 4.95% commission.
Total sales at this level is $300,000
[tex]\begin{gathered} \text{Commision made on the next \$200,000 is;} \\ \frac{4.95}{100}\times200000=\text{ \$9,900} \\ =\text{ \$9,900} \end{gathered}[/tex]On the next $87,000, total sales at this level is $387,000. She earns 7.25% commission for sales above $300,000.
[tex]\begin{gathered} \text{Commision made on the next \$87,000 is;} \\ \frac{7.25}{100}\times87000=\text{ \$6,}307.50 \\ =\text{ \$6,}307.50 \end{gathered}[/tex]Therefore, Susan's total commission received for the month is;
[tex]\begin{gathered} \text{ \$1250 + \$9900 + \$6307.50} \\ =\text{ \$17,457.50} \end{gathered}[/tex]Hence, her commission received in total for the sales made is $17,457.50
Teresa surveyed 100 students about whether they like pop music or country music. Outof the 100 students surveyed, 42 like only pop, 34 like only country, 15 like both popandcountry, and 9 do not like either pop or country. Complete the two-way frequency table.
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SOLUTION
Write out the given information
[tex]\begin{gathered} \text{Total number of student surveyed=100} \\ \text{like pop only=42} \\ \text{like country only=34} \end{gathered}[/tex][tex]\begin{gathered} \text{like both pop and country=15} \\ Do\text{ not like any =9} \end{gathered}[/tex]Construct the two- way frequency table
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!
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Answer:
A. reflection over the y-axis
B. translation 3 units right
C. translation 4 down
D. reflection over the x-axis
1. Jessica finishes her book in 2 1
3
hours. Eric takes 11
2
times longer than
Jessica to finish his book.
This model represents the amount of time Jessica takes to finish her
book. It has a width of 1 and a length of 2 1
3
. The model is 2 1/3 out of 3
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The time taken for Eric to finish the book is 3 1/2 hours.
What is a fraction?A fraction simply means a part of a whole. It van also refer to any number of equal parts.
The information illustrated that Jessica finishes her book in 2 1 / 3 hours and that Eric takes 1 1 / 2
times longer than Jessica to finish his book.
In this case, the time that was used by Eric will be the multiplication of the fractions given. This will be illustrated as:
= 2 1/3 × 1 1/2
Change to improper fraction
= 7/3 × 3/2
= 7 / 2
= 3 1 / 2
Eric used 3 1/2 hours.
This illustrates the concept of multiplication of fractions.
The complete question is written below.
Learn more about fractions on:
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Jessica finishes her book in 2 1/3.hours. Eric takes 1 1/2 times longer than Jessica to finish his book. How long did Eric take yo finish the book?
Hurry and answer this pls Bc this have to be turned in
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Each year, a scientist measures the water level of a local lake. Negative numbers indicatethat the water level is below its historical average. Which list shows the water levels in orderfrom highest to lowest?0.7, 0.38, 0.09, – 0.41, – 0.60.7, 0.38, 0.09,-0.6,- 0.41-0.6, 0.38, – 0.41, 0.09, 0.70.38, 0.09, 0.7,– 0.6 – 0.410.38, 0.7, 0.09 – 0.41, -0.6
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Answer:
-0.6, -0.41, 0.09, 0.39, 0.7
Step-by-step explanation:
Negative numbers: The higher the absolute number, the lower it is. For example, -2 is lower than -1.
Positive numbers: The lower the absolute number, the lower it is. For example, 1 is lower than 2.
In this question:
We have these following values:
0.7, 0.39, 0.09, -0.41, -0.6
Ranking from lowest to highest, it is:
-0.6, -0.41, 0.09, 0.39, 0.7
May I please get help with numbers (4), (5), and (6). I have tried multiple times to find the correct answers for each of them but still could not get the accurate or at least correct answers for each of them. I would appreciate it so much if I could get help
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EF =21
4) Let's find out the measure of the line segment EF, using the Trapezoid Midsegment Formula:
[tex]M=\frac{B+b}{2}[/tex]4.1) We can plug into that the lengths of AD and BC:
[tex]M=\frac{18+24}{2}=\frac{42}{2}=21[/tex]Note that the Midsegment is the average of the bases of a trapezoid.
4.3) Hence, the answer is 21
determine the missing angle measures in each triangle
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ANSWER:
50°
STEP-BY-STEP EXPLANATION:
We can calculate the value of the missing angle, since there is a right angle (that is, 90°) and the other is 40 °, we apply the property that says that the sum of all the internal angles of a triangle is equal to 180°, Thus:
[tex]180=90+40+x[/tex]Solving for x:
[tex]\begin{gathered} x=180-90-40 \\ x=50\text{\degree} \end{gathered}[/tex]For the given f(x), solve the equation f(x)=0 analytically and then use a graph of y=f(x) to solve the inequalities f(x)<0 and f(x)≥0. f(x)=ln(x+3)(1) What is the solution of f(x)=0?(2) What is the solution of f(x)<0?(3) What is the solution of f(x)≥0?
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Explanation:
f(x) is a logarithmic function. Logarithmic functions are zero when the argument is 1:
[tex]\begin{gathered} f(x)=\ln (x+3)=0 \\ x+3=1 \\ x=1-3 \\ x=-2 \end{gathered}[/tex]For greater values, the function is positive and for less values the function is negative.
Answers:
(1) x = -2
(2) x < -2. In interval notation x:(-∞, -2)
(3) x ≥ -2. In interval notation x:[-2, ∞)
Tyler said he swam 23 tenths miles this week. His coach said Tyler swam 2.3 miles this week. To find who is correct, model the distance both Tyler and his coach said Tyler swam. Use the flat as 1 unit. A: What do you need to use?B: What do you know about representing whole numbers and decimals that may help you solve the problem? C: Complete the sentencesAre the models alike or different?Tyler swam _____ tenths, or _____, miles.So, _____________________ are correct.
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Answer with explanation:
We need to determine if what Tyler is saying is in fact equal to what his coach said, to get the final answer, we have to concert the resulting units in miles:
Taylor's answer:
[tex]23\times(\frac{1}{10})\text{ miles}\Rightarrow(\frac{23}{10})\text{miles}\Rightarrow2.3\text{ miles}[/tex]Coach's answer:
[tex]2.3\text{ miles}[/tex]In conclusion, The two answers are correct so the two models are indeed alike.
Ava graphs the function h(x) = x^2 + 4. Victor graphs the function g(x) = (x + 4)^2. Which statements are true regarding the two graphs? Select three options.Ava’s graph is a vertical translation of f(x) = x^2.Victor’s graph is a vertical translation of f(x) = x^2.Ava’s graph moved 4 units from f(x) = x^2 in a positive direction.Victor’s graph moved 4 units from f(x) = x^2 in a positive direction.Ava’s graph has a y-intercept of 4.
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Given,
Ava graphs the function h(x) = x^2 + 4.
Victor graphs the function g(x) = (x + 4)^2.
Required:
Check the correct statement about graph.
The graph of Ava and vector function is:
Here, victor graph was represented by blue curve and ava graph by green curve.
For first statement,
Ava’s graph is a vertical translated by 4 units.
Hence, statement is true.
For second statement,
The graph of victor is not vertically translated.
Hence, statement is false.
For statement three,
The curve of the Ava graph is moved 4 unit up in the positive direction. It is in y axis. Hence, statement is true.
For statement forth,
The curve of the victor graph is moved to negative direction not positive. Hence, statement is false.
For statement fifth,
The graph of Ava has the y intercept at 4. So, statement is correct.
Hence, option A (Ava’s graph is a vertical translation of f(x) = x^2), option C (Ava’s graph moved 4 units from f(x) = x^2 in a positive direction) and option E (Ava’s graph has a y-intercept of 4.) is true.
what is the LCM of 4 and 6 ?
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LCM stands for Least Common Multiple.
And it is defined as the product of the two numbers divided by the GCD (greatest common divisor)
In our case, the product of 4 and 6 is 24, , and the greatest common divisor of 4 and 6 is "2". Therefore, the LCM of 4 and 6 is 24/2 = 12
Let me also use the Venn diagram that your teacher provided:
In the diagram we enter the factors that correspond to both numbers (4 and 6), and in the intersection of the two sets (intersection of the circle) we type a "2" which is the ONLY factor 4 and 6 have in common (the greatest common divisor of the two given numbers) So complete a diagram as follows:
We typed a 2in the area common to both numbers. Then your LCM is the product of 2 times 2 times 3 = 12
Notice the blue set (circle) contains the two factors for 4 (2 * 2) and the orange circle contains the two factor for 6 (2 * 3)
We set in the intersection of the two circles the factor that is common to both.
Do you want me to complete the second question with a Venn diagram as well? Perfect.
The second question is about the LCM of the numbers 12 and 8
Then we create a Venn diagram like the following, considering that the factor in common between 12 and 8 is 4, because 12 = 4 * 3 and 8 = 4 * 2
Again here, the factors 3 and 4 (that give 12) are typed in the blue circle. and the factors that form 8 (4 * 2) are typed inside the orange circle.
The factor that both share is in the middle "4". Therefore, now to find the LCM you simply multiply the three numbers shown in the Venn diagtam: 3 * 4 * 2 = 24
Then 24 is your LCM.
How do I know which score is the highest frequency? how do I figure the scores had a frequency of 2?
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To determine the score which presents the highest frequency, we need to check the last column, the frequency one, and find the highest value among them. The score which is in the same row that this value will be the score with the highest frequency.
In the present problem, there are values of frequency equal to 1, 2, 3, and 4. The one with frequency 4 is the one with the highest frequency. (8th row). And the Score related to it is Score 8.Once we check the frequency column once again, we see that the 2nd, the 4th, and the 7th rows have a frequency equal to 2.
Checking the Scores of the related rows, we are able to say that the scores with frequency 2 are: 2, 4, and 7.How do I tell if a parabola has a minimum or a maximum?
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We can write the equation of a parabola in two different ways:
The standard form:
[tex]\begin{gathered} y=ax^2+bx+c \\ a\ne0 \end{gathered}[/tex]And the vertex form:
[tex]y=a(x-h)^2+k[/tex]If the parabola has a minimum or a maximum depends on the leading coefficient (the coefficient of x²) or in both cases the coefficient a.
Let's see the cases:
[tex]a>0_{\text{ }}(a_{\text{ }}is_{\text{ }}positive)[/tex]If a is positive, the parabola opens upwards, so the parabola has a minimum.
[tex]a<0_{\text{ }}(a_{\text{ }}is_{\text{ }}negative)[/tex]If a is negative, the parabola opens downwards, so the parabola has a maximum
NEED HELP ASAP
What is the value of X? Justify each step
Answers
The value of x = 3 ,where ,
AC = 32 , AB = 2x , BC = 6x + 8 .
Solution:Here given,
AB = 2x
BC = 6x + 8
AC = 32
AC = (AB + BC) (Rule of addition).
So ,
2x + 6x + 8 = 32 (by applying substitution rule) .
In the equation AB + BC = AC, substitute for AB, BC, and AC.
Simplifying,
8x + 8 = 32
2x + 6x + 8 = 32 (when simplified by incorporating similar terms).
8x = 24
8x = 32 - 8
8x = 24
On dividing both sides by 8
8x / 8 = 24/8
x = 3
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Joseph owns a 50 inch TV and it measures 50 inch on the diagonal. if the television is 40 inches across the bottom find the height of the TV
Answers
Let's draw the tv with the given values.
Note that we will form a right triangle with heigh of h, base of 40 and a hypotenuse of 50.
The Pythagorean Theorem is :
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse, a and b are the legs of the triangle.
Using the formula above. we will have :
[tex]\begin{gathered} 50^2=40^2+h^2 \\ 2500=1600+h^2 \\ h^2=2500-1600 \\ h^2=900 \\ \sqrt[]{h^2}=\sqrt[]{900} \\ h=30 \end{gathered}[/tex]The answer is 30 inches