Answers
The zeros of the quartic equation x⁴ - 2 · x² - 63 are x₁ = √(1 - √62), x₂ = √(1 + √62), x₃ = - √(1 - √62) and x₄ = - √(1 + √62).
How to find the zeros of a quadratic like quartic equation by factorization
In this problem we find a quadratic-like quartic equation, that is, a quadratic equation of the form:
y = a · x⁴ + b · x² + c
Where a, b, c are real coefficients.
From this expression in standard form we must determine its roots by using an application of algebra properties known as completing the square, which is transforming a part of the function into cubic square trinomial.
First, write the expression and equal it to zero:
x⁴ - 2 · x² - 63 = 0
Second, complete the square and simplify:
(x⁴ - 2 · x² + 1) = 63 - 1
(x² - 1)² = 62
x² - 1 = ± √62
x² = 1 ± √62
x = ± √(1 ± √62)
Third, write all the zeros of the quartic equation:
x₁ = √(1 - √62), x₂ = √(1 + √62), x₃ = - √(1 - √62), x₄ = - √(1 + √62)
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Related Questions
What is the interest earned in a savings account for 12 months on a balance of $4000 of the interest rate is 1.5% APR compounded earlier
Answers
answer: 60.00
Based on the given conditions, formulate:: 4000x
((1.5%+1)12/12-1)
Evaluate the equation/expression:: 60
Round 60 to the required place rounding: 60.00
How much firewood is sold per year in us
Answers
Dwayne's percentage favorite eatery. Overall, the restaurant had 25 specials, with salmon filets accounting for 24% of those. The eatery served 6 salmon filets.
What do percentages actually mean?10% is a comparison number that means one tenth of any amount. The hundredth component, one percent (symbolized as 1%), is denoted by 100 percent, whereas 200 percent denotes double the quantity stated. In mathematics, a percentage is a number or ratio that may be expressed as a fraction of 100. If we want to calculate a percentage of a number, we should multiply the result by 100.
Dwayne's favorite eatery. Overall, the restaurant had 25 specials, with salmon filets accounting for 24% of those. The eatery served 6 salmon filets.
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what’s the area of a semi circle
Answers
Answer:
14.13
Step-by-step explanation:
Since we know the area of a circle is [tex]\pi r^2[/tex], we just need to divide it by 2 to get the semicircle's area ( [tex]\frac{\pi r^2}{2}[/tex] )
We know the radius is equal to half of the diameter, or in this case 3, and we're approximating pi to 3.14, so we just substitute on the formula:
[tex]\frac{(3.14)(3)^2}{2} = \frac{(3.14)(9)}{2} = \frac{28.26}{2} = 14.13[/tex]
378 divided by 5 find the quotient and remainder
Answers
When 378 divided by 5 the quotient is 75 and the remainder is 3.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, dividend =378 and divisor =5.
Now, 378/5
5|378|75
375
______
3
Here, the quotient is 75 and the remainder is 3
Therefore, when 378 divided by 5 the quotient is 75 and the remainder is 3.
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I need help with this question please and thank you
Answers
Answer:
A proportional graph is a straight line that goes through the origin (0,0).\
Based on this information, the only correct answers would be B and C.
Okay im learning algebra right now and this question hit my head
here, its asked which expression was equivalent to this 2v+6v+3c.
here are the answer 2v + 9c 8v + 3c 11vc 11+ v+ c
Answers
Answer:
8v+3c
Step-by-step explanation:
2v+6v+3c
2v and 6v have similar figures so you can add them together
so it becomes 8v+3c
c and v have nothing in common so you cannot simplify them more
a company believes that travel agent a is more reliable than travel agent b. that belief is expressed on a scale from 1 to 5. identify the type of data.
Answers
The type of data expressed in the example is ordinal data.
This is an example of ordinal data, as it is data that is expressed on a scale from 1 to 5. Ordinal data is useful for comparing objects or ideas in relation to each other, and is often used to indicate levels of preference or satisfaction. In this case, the data is used to compare the reliability of two travel agents.
Ordinal data is a type of data where the values are ranked in order of magnitude. In the example given, the company has expressed their belief on a scale from 1 to 5, with higher numbers representing a higher level of reliability. Therefore, this type of data is considered ordinal.
The type of data expressed in the example is ordinal data.
Ordinal data is a type of data where the values are ranked in order of magnitude.
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consider the data below: 12 45 35 45 24 34 65 43 23 43 a.) find p20 b.) find p67 c.) find the percentile corresponding to 34 d.) create a boxplot
Answers
a) P20 is the 20th percentile, which separates the lowest 20% of the data from the highest 80%. To find P20, you would need to put the data in numerical order and find the value at the 20th percentile.
b) P67 is the 67th percentile, which separates the lowest 67% of the data from the highest 33%. To find P67, you would need to put the data in numerical order and find the value at the 67th percentile.
c) 34 is the 34th percentile, which separates the lowest 34% of the data from the highest 66%. It is the value at the 34th percentile
d) A boxplot is a graphical representation of a dataset that shows the minimum, first quartile, median, third quartile, and maximum of the data. To create a boxplot, you would need to put the data in numerical order, then calculate the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum of the data. These values are then plotted on a graph, with the box representing the interquartile range (Q3 - Q1) and the whiskers representing the minimum and maximum values. The outliers(if any) will be plotted as dots
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Are the following functions inverses of one another ?
Use function composition to explain your answer :)
Answers
Yes, the given functions are inverses of one another.
What is inverse function?Inverse function is represented by with regards to the original function and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.
The given functions are f(x)=5x+2 and g(x)=(x-2)/5.
The function f(x)=5x+2 can be written as y=5x+2
Swap x and y positions, we get
x=5y+2
x-2=5y
y=(x-2)/5
Therefore, the function g(x) is the inverse function os f(x).
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Adam bought a $1,670 custom video game/sound system on a special interest plan. He made a $100 down payment and agreed to pay the entire purchase off in 12 years. The minimum monthly payment is $10. If he makes the minimum monthly payment up until the last payment, what will be the amount of his last payment?
Answers
Adam will be paying by installment, and will pay the amount of $140 of his last payment if he pays the $10 minimum monthly payment up until the last payment.
What is payment by installmentPayment by installment is when one pay small sums of money at regular intervals over a period of time, rather than paying the whole amount at once.
Adam made a down payment of $100 out from the total amount of $1,670, so he will have to pay a balance of $1570 in 12 years.
The minimum monthly payment is $10, and he will have 144 months to pay up the balance.
If Adam pays $10 for 144 months, he will pay up a total of $1440 having a balance of $130 to pay after the deadline.
Therefore, if Adam makes the minimum monthly payment up until the last payment, he would have paid up $1430 which is $10 in 143 months and will pay the amount of $140 of his last payment.
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Perry won 58 lollipops playing basketball
at his school's game night. Later, he gave
three to each of his friends. He only has
10 remaining. How many friends does he
have
Answers
The friends does perry have could be 16.
What is linear equation ?
linear equation if the highest degree of an equation is 1 , it is called as linear equation .
Given perry won 58 lollipops playing basketball .
He later gave three to each of his friends.
lets his number of friends could be x .
so,
58 - 3x = 10
3x = 58 - 10
3x = 48
x = 16
Hence the friends does perry have could be 16
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The friends does perry have could be 16.
What is linear equation ?linear equation if the highest degree of an equation is 1 , it is called as linear equation .
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two parts, separated by an equals sign (=). For example, the equation 2x + 3 = 7 is a statement that the expression 2x + 3 is equal to the expression 7.
Given perry won 58 lollipops playing basketball .
He later gave three to each of his friends.
lets his number of friends could be x .
so,
58 - 3x = 10
3x = 58 - 10
3x = 48
x = 16
Hence the friends does perry have could be 16
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Please assist asap, it’s a 6 point question!
Answers
Answer: The equation of the perpendicular bisector of AB is 3x+7y-77=0
A line equation is an algebraic representation of a set of points that together form a line in a coordinate system. Multiple points that together form a line on the coordinate axis are represented as a set of x,y variables to form an algebraic equation called a one-line equation.
Equation of line⇒[tex](y-y1)=\frac{(y2-y1)}{(x2-x1)} (x-x1)[/tex]
Midpoint of line⇒[tex]\frac{(x1+x2)}{2}, \frac{(y1+y2)}{2}[/tex]
Step-by-step explanation:
Line CD⊥AB
Equation of AB⇒ [tex]\frac{y+10}{x-4} =\frac{15-1}{10-4} \\[/tex]
⇒ [tex]\frac{y+10}{x-4} =\frac{14}{6}[/tex]
⇒ [tex]\frac{y+10}{x-4} =\frac{7}{3}[/tex]
⇒ 3(y+10)=7(x-4)
⇒ 3y+30=7x-28
⇒ 7x-3y=30+28
⇒ 7x-3y=58
Midpoint of AB⇒ [tex]\frac{4+10}{2} , \frac{1+15}{2}[/tex]
⇒ [tex]\frac{14}{2}, \frac{16}{2}[/tex]
⇒ (7, 8)
Slope of CD⇒ [tex]\frac{-1}{slope of AB}[/tex]
Slope of AB⇒ [tex]\frac{-7}{-3}[/tex]
⇒ [tex]\frac{7}{3}[/tex]
Slope of CD⇒ [tex]\frac{-3}{7}[/tex]
Equation of CD⇒ [tex]y-8=\frac{-3}{7} (x-7)[/tex]
⇒ 7(y-8)=-3(x-7)
⇒ 7y-56=-3x+21
⇒ 3x+7y-56-21=0
⇒ 3x+7y-77=0
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A fast food restaurant just leased a new freezer and food fryer for three years. The service contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 service charge for each repair needed. The restaurant’s research indicates that during a given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% twice, 4% three times, and none required more than three repairs.
a. Find the expected number of repairs for this freezer per year.
b. Find the standard deviation of the number of repairs per year.
c. What are the mean and standard deviation of the restaurant’s annual expense with the service contract for the freezer?
Answers
(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.
What is Standard Deviation?Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.
(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.
E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)
= 0.33
(b) Standard deviation of number of repairs per year can be calculated as,
SD(Repairs) = [tex]\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }[/tex]
= √ (0.5611)
= 0.749
(c) Mean of the restaurant's annual expense with service contract is,
Mean = Expected cost = $125 + ($35 × 0.33) = $136.55
Standard deviation of the restaurant's annual expense with service contract is,
SD = [tex]\sqrt{35^{2}(0.5611) }[/tex] = 35 × 0.759 = 26.217
Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.
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Which is a solution to the equation x² 4x +4 0?
Answers
Therefore , the solution of the given problem of quadratic equation comes out to be yields the final response. x=2 several roots.
What is quadratic equation?The quadratic solution x = ax2 + foo + c=0 is a regression model for one variable equations. According to the First Theorem of Algebra, this polynomial only has one solution because of its second order. Both straightforward and complex solutions are viable options. The term "quadratic formula" refers to a formula with four variables. According to this, there can only be a single squared word present. Mathematical variables or variables a, b, and c are often used to represent the unknown variable "X" in the formula "ax2 + bx + c = 0," which is frequently used to solve arithmetic problems.
Here,
Use the quadratic formula to find the solutions.
−b±√b²−4(ac)/2a
Substitute the values
a=1, b=−4, and
c=4
into the quadratic formula and solve for
x.4±√(−4)²−4⋅(1.4) / 2⋅1
Simplify.
Simplify the numerator.
x=4/2⋅1
Multiply 2 by 1
x=4/2
Divide 4 by 2
x=2
The combination of the two solutions yields the final response. x=2 several roots.
Therefore , the solution of the given problem of quadratic equation comes out to be yields the final response. x=2 several roots.
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Benito has a job that pays $14.15 per hour for a 40-hour work week. He is to be paid time and a half for every hour over 40 that he works in a week. What will his gross pay be for a week in which he works 49 hours?
Answers
Benito's gross pay for the week will be $757.07.
What are work and time?
In aptitude, work and time are related concepts that are used to calculate the rate of work being done.
Benito is to be paid time and a half for every hour over 40 that he works, so for a 49-hour work week, he will be paid for 49 - 40 = 9 hours of overtime.
His regular pay for the first 40 hours is $14.15 per hour * 40 hours = $566.
His overtime pay is $14.15 per hour * 1.5 = $21.23 per hour
His overtime pay for 9 hours is $21.23 per hour * 9 hours = $191.07
his gross pay for the week will be $566 + $191.07 = $757.07.
Hence, Benito's gross pay for the week will be $757.07.
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Aiden has $15.00 on his copy card. Each time he uses the card to make a photocopy, $0.06 is deducted from his card. Aiden wants to be sure that there will be at least $5.00 left on his card when he is finished. The inequality below relates x, the number of copies he can make, with his copy card balance. What is the maximum number of copies Aiden can make
Answers
Aiden can make up to 166 copies before his copy card balance reaches below $5.00 as each copy total costs $0.06.
1. 15.00 - 0.06x ≥ 5.00
2. Add 0.06x to both sides: 15.00 ≥ 0.06x + 5.00
3. Subtract 5.00 from both sides: 10.00 ≥ 0.06x
4. Divide both sides by 0.06: 166.67 ≥ x
5. Therefore, x ≤ 166.67, so Aiden can make a maximum of 166 copies.
Aiden's copy card balance is $15.00, and each copy he makes costs $0.06. To ensure that his card balance does not go below $5.00, he needs to calculate the max number of copies he can make. To do this, we set up an inequality, 15.00 - 0.06x ≥ 5.00, and solved it to get x ≤ 166.67, meaning Aiden can make a maximum of 166 copies.
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During the season, the number of goals Keon scored to
the number of goals Max scored was 3 to 4. If Max
scored 16 goals, how many goals did Keon score?
Answers
Keon scored 5 goals.
In this question, all measurements are in millimetres.
An equilateral triangle has side lengths of 4a + 2.
A square has side lengths of 2a + 7.
Given that the triangle has a larger perimeter than the square, work out the
smallest possible integer value that a could take.
+
Answers
The smallest possible integer value that 'a' could take is 6.
What is Perimeter?Perimeter is the total length of a shape's boundary.
Perimeter of equilateral triangle = 3a, where a is the side length
Perimeter of a square = 4b, where b is the side length
Let P₁ be the perimeter of equilateral triangle and P₂ be the perimeter of square.
Here,
Length of side of equilateral triangle = 4a + 2
P₁ = 3 (4a + 2)
Length of side of square = 2a + 7
P₂= 4 (2a + 7)
Given P₁ > P₂
3 (4a + 2) > 4 (2a + 7)
By distributive property,
12a + 6 > 8a + 28
12a - 8a > 28 - 6
4a > 22
a > 22/4
a > 5.5
Hence 6 is the smallest number which is an integer that 'a' could take.
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20÷5+4x7-4 help plis
Answers
Answer:
28 / Ounce of wed >;)
Step-by-step explanation:
Answer:
28
Step-by-step explanation:
PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction)
Multiply 4 and 7 (28), divide 20 by 5 (4), add those together (32) and then subtract 4 which will get you 28
find the valeu of r if 5(r-3)=20
Answers
The value of [tex]r[/tex] is [tex]7[/tex]
The given equation is
[tex]5(r-3)=20[/tex]
We will now open the bracket, [tex]5r-15=20[/tex]
Let's simplify,
[tex]5r=20+15\\5r=35\\r=\frac{35}{5} \\r=7[/tex]
The value of [tex]r=7[/tex]
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X by the power of 2 -36
Answers
The solutions of x²=-36 are 6i and -6i.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
X by the power of 2 is -36
This can be written as x²=-36
We need to find the value of x.
x²=-36
Take square root on both sides
x=√-36
x=√i²36
x=6i, -6i
Hence, the solutions of x²=-36 are 6i and -6i.
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the bearing of B from A is 162. Work out the bearing of A from B
Answers
Answer: 180°
Step-by-step explanation:
If given the bearing from B to A, the bearing from A to B can be found using interior angles. Subtract the bearing of B to A from 180° to find the missing interior angle, then use the fact that angles in a full turn add to 360° to find the bearing of A to B.
X
————————
Y
Formula of the Line
Answers
Answer:
y = 4x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept, where it crosses the y- axis )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (- 2, - 4) ← 2 points on the line
m = [tex]\frac{-4-0}{-2-(-1)}[/tex] = [tex]\frac{-4}{-2+1}[/tex] = [tex]\frac{-4}{-1}[/tex] = 4
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 4x + 4 ← equation of line
Name the quadrant in which the angle theta lies.
cos theta > 0, sec theta < 0
Choose the correct answer below.
A. The angle theta lies in quadrant II.
B. The angle theta lies in quadrant III.
C. The angle theta lies in quadrant I or III.
D. The angle theta does not exist.
Answers
The angle theta lies in quadrant I or III.
Hence, option (C) is the correct choice.
The coordinate system's two axes, the x-axis and the y-axis, constitute an area called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes.
Cosθ=(1/Sinθ)
And, Secθ = (1/Cosθ)
As we know,
In the first Quadrant.
The value of Sinθ is positive, so the corresponding value of Cosθ will be also Positive.
As, In the second case the value of Secθ should be less than 0,
We know the value of Cosθ is negative in the third Quadrant.
So, the value of the Secθ will be less than 0 in the third quadrant.
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Logarithm question (picture included)
Answers
Base 3 logarithm of 81 equals 4 .The logarithmic form, written as log of "b" to base "a" is equal to "n," .
what is logarithm ?How many times must one "base" number be multiplied by itself in order to get another specific number is the subject of the mathematical expression known as a logarithm (or log). Mathematics includes both logarithms and logs. They share a connection with exponential functions. Logarithms are the opposite of exponentiation because they reveal the exponent (or power) required to create a given number. They were helpful in the past for splitting or multiplying huge numbers.
given
Base 3 logarithm of 81 equals 4 .
Therefore, the logarithmic form, written as log of "b" to base "a" is equal to "n," may be expressed in exponential form as a = b.
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Suppose a varies directly as b, and a=7 when b=2. Find b when a=21
Answers
The value of [tex]b=6[/tex]
It is given that [tex]a[/tex] varies directly to [tex]b[/tex]
So, we can write [tex]a=kb[/tex] ([tex]k[/tex] = constant)
We know that [tex]a=7[/tex] when [tex]b=2[/tex]
that is [tex]7= 2k[/tex]
[tex]k=\frac{7}{2}[/tex]
so when [tex]a=21[/tex]
[tex]a=kb[/tex]
substitute the value of [tex]a[/tex] and [tex]k[/tex]
that is [tex]21=\frac{7}{2} b[/tex]
[tex]b=6[/tex]
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7. Use the dot product to determine which of the following vector pairs are orthogonal.
A. V1=(22,15) and v2=(-2,4)
Part 1: Multiply the two x-coordinates of the vectors and the 2Y coordinates of the factors. Write each product below. (2 points)
Part II: add the two products together. What is the result? (2 points)
Part III: are the two vectors orthogonal? (2 points)
Answers
Vectors V1=(22,15) and v2=(-2,4) are not orthogonal.
What are Orthogonal Vectors?Two vectors are said to be orthogonal if they are perpendicular
to each other. i.e. the dot product of the two vectors is zero.
Given vectors are:
V₁ = (22,15)
V₂ = (-2,4)
Dot product of V₁ and V₂ = (22,15).(-2,4) = 22×-2 + 15×4
Part 1:
Multiplying x-coordinates of vectors-
(22×-2) = -44
Multiplying y-coordinates of vectors-
(15×4) = 60
Part 2: Adding the products = -44+60 = 16
Part 3: If the dot product of two vectors is zero, then the two vectors are orthogonal.
But the dot product from the above calculation is 16 means vectors are not orthogonal.
Hence, the two vectors are not orthogonal.
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What percentage of the shape is blue?
Write your answer using a percent sign (%).
Answers
13/20=x/100
20x=1300
20x/20=x 1300/20=65
So x=65%
What are the 4 quadratic methods?
Answers
The 4 quadratic methods are factoring, completing the square, using the quadratic formula, and graphing.
Quadratic equations are a type of mathematical equation that can often be solved using a variety of methods. The four main methods used to solve quadratic equations are factoring, completing the square, using the quadratic formula, and graphing.
Factoring is a method that involves finding the factors of the quadratic equation in order to solve for the variables.
Completing the square is a method that involves rewriting the equation in the form of (x + a)² = b in order to solve for the variables. The quadratic formula is a method that involves using the formula ax² + bx + c = 0 to solve for the variables.
Finally, graphing is a method that involves plotting the equation on a graph and analyzing the graph in order to solve for the variables.
These four methods are the main ways to solve quadratic equations, and each method has its own set of advantages and disadvantages.
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In the figure, angle A measures 38
degrees and angle D measures 26
degrees. What is the measurement of angle E?
Answers
Answer:
E = 102
Step-by-step explanation:
1) Write down what angles you already know
A = 38 (given)
D = 26 (given)
B = 90
2) Work out the angles in the triangle
A triangle has 180 degrees so...
38 + 90 = 128180 - 128 = 523) Work out the angles on the straight line
From the previous calculation we know that C = 52 (as it was the remaining angle)
Angles on a straight line should add up to 180 and we are given that D = 26...
52+26 = 78180 - 78 = 102E = 102Hope this helps, have a great day!
Answer:
Angle E = 102°
Step-by-step explanation:
In the figure, angle A measures 38
degrees and angle D measures 26
degrees. What is the measurement of angle E?
the sum of the internal angles of a triangle is 180°, we know that the angle B measures 90° and the angle A measures 38°, we subtract the angles A and B from 180° and we find the angle C
180 - 38 - 90 = 52° (Angle C)
now that we have angle C and angle D we can find angle E. they are all on a straight line, so the sum is 180°, from 180° we subtract angle C and D and we have angle E180 - 52 - 26 = 102 (Angle E)
---------------------------
check
D + C + E = 180
26 + 52 + 102 = 180
180 = 180
the answer is good
the other answer is wrong