Answers
All of the triangles are an isosceles triangle, which means that they have two congruent side, and two congruent angles.
The first triangle has ∠B as 56°, AB ≅ BC.
The angle opposite to AB and BC are therefore, congruent, which means that
∠A + ∠B +∠C = 180°
∠A + 56° + ∠A= 180° (∠A and ∠C are congruent)
2∠A = 180° - 56°
2∠A = 124
∠A = 62°
The second triangle has ∠C equal to 62°. Since ∠A and ∠Care the angle opposite to the congruent side, they are also congruent which means ∠A = 62°.
The fourth triangle which has an exterior angle of ∠C equal to 118° forms a linear pair, and are thus supplementary
∠C = 62°, and both ∠C and ∠A are the corresponding angles to the congruent sides, it follows that they are also congruent.
∠A = 62°.
Conclusion
The following triangles have m∠A = 62°, first, second, and fourth triangle.
Related Questions
just 34 unless you want to help me with more?
Answers
M is the midpoint of the line segment FG.
Being the midpoint means that M divides the line in two equal halves so you know that the distance between F and M is equal to the distance between M and G, symbolically:
FM=MG
And of you add them you'll be able to calculate the length of the whole line FG
34.
Given the expressions
FM= 5y+13
MG=5-3y
We know that FM=MG, so the first step is to replace this equivalency with the given expressions. This way you'll determine an equation with one unknown y.
Once you have the equation you can clear the value of y:
[tex]\begin{gathered} FM=MG \\ 5y+13=5-3y \end{gathered}[/tex]Pass all terms with the unknown to one side of the equation and all others to the other side:
[tex]\begin{gathered} 5y+3y=5-13 \\ 8y=-8 \\ y=-1 \end{gathered}[/tex]y=-1
Now that you know the value of y, you can replace it in the given expressions to calculate the length of FG
[tex]\begin{gathered} FG=FM+MG \\ FG=(5y+13)+(5-3y) \\ FG=5y+13+5-3y \\ FG=2y+18 \\ \text{Replace with y=-1} \\ FG=2(-1)+18 \\ FG=16 \end{gathered}[/tex]The length of the line segment FG is 16 units.
Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Write the around it to two decimal places if necessary.8i4 + 5i
Answers
SOLUTION
The given complex expression is:
[tex]\frac{-8i}{4+5i}[/tex]Rationalize the denominator
This gives
[tex]\begin{gathered} \frac{-8i}{4+5i}\times\frac{4-5i}{4-5i} \\ =\frac{-32i-40}{16+25} \\ =-\frac{40}{41}-\frac{32i}{41} \end{gathered}[/tex]can you give me some examples of how to simplify
Answers
Let's check out the expression
[tex]2x+4+6y+7+2+3x[/tex]To simplify, you have to add up similar terms. That is, add up everything that has an x, add up everything that has a y, and add up every independent term (no variable), as following:
[tex]\begin{gathered} 2x+4+6y+7+2+3x\rightarrow2x+3x+6y+4+7+2 \\ \rightarrow5x+6y+13 \end{gathered}[/tex]And there we have the simplified expression.
The table shows a proportional relationship.
x 12 8 24
y 3 2 6
Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (3, 12).
A line passes through the point (0, 0) and continues through the point (2, 8).
A line passes through the point (0, 0) and continues through the point (6, 24).
A line passes through the point (0, 0) and continues through the point (12, 3).
Answers
A graph of which best describes what the proportional relationship would look like is: D. A line passes through the point (0, 0) and continues through the point (12, 3).
What is a graph?In Mathematics, a graph is used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
Additionally, a graph that represents a proportional relationship between two variables would always have a straight line with its data points passing through the origin (0, 0).
Since the graph represents a proportional relationship we have:
Constant of proportionality, k = 12/3 = 8/2 = 24/6 = 4
Ratio = 24:6 = 12:3.
Therefore, (0, 0) and (12, 3) are points on this graph that represents a proportional relationship.
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Answer:d
Step-by-step explanation:trust
Help please and thank you
Answers
Hence coordinates of x interfept = (-2,0)
On the y intercept, the x coordinate is 0. Hence 4(0) -2y = -8
-2y= -8
y=-8/-2 = 4
Y intercept coordinate is (0.4)
Roseanne makes 1 1/2 of strawberry lemonade. She pours 1/4 of a liter of lemonade into a thermos to take to the park. Her brother drinks 2/5 of the remaining lemonade. How much lemonade does Roseanne's brother drink? Which expression can be used to determine the amount of lemonade Roseanne's brother drank? A. 1 1/2 - (1/4 x 2/5) B. (1 1/2 + 1/4) x 2/5 C. (1 1/2 - 1/4) x 2/5 D. (1 1/2 - 1/4) ÷ 2/5
Answers
we know that
the total lemonade is 1 1/2 liter
She pours 1/4 of a liter of lemonade into a thermos
Her brother drinks 2/5 of the remaining lemonade
the remaining lemonade is equal to
1 1/2-1/4=3/2-1/4=5/4 liters
Multiply by 2/5
(5/4)(2/5)=10/20=1/2 liter
therefore
answer is option
C. (1 1/2 - 1/4) x 2/5
twice the difference of a number 4 is 5.
Answers
Answer:25
Step-by-step explanation:
Hello I need help please.The choices for f(-6): A. f(-6) ; B. The answer is not a real number
Answers
Given the function:
[tex]f\mleft(x\mright)=\sqrt{x-1}[/tex]First part:
You need to substitute the following value of "x" into the function:
[tex]x=1[/tex]In order to find:
[tex]f(1)[/tex]Then, substituting and evaluating, you get:
[tex]\begin{gathered} f(1)=\sqrt[]{1-1} \\ f(1)=\sqrt[]{0} \\ f(1)=0 \end{gathered}[/tex]Second part:
Substitute this value of "x" into the function:
[tex]x=-6[/tex]And then evaluate, in order to find:
[tex]f(-6)[/tex]You get:
[tex]\begin{gathered} f(-6)=\sqrt[]{-6-1} \\ f(-6)=\sqrt[]{-7} \end{gathered}[/tex]Since the Radicand is negative, it is not a Real Number.
Therefore, the answers are:
First part:
A.
[tex]f(1)=0[/tex]Second part:
B. The answer is not a real number.
HELP ME WITH IS PROBLEM THANK YOU
Answers
The solution to the given expression is 10√5 - 4√10 which is the correct answer would be an option (C)
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
The given expression as:
⇒ √5(10 - 4√2)
Open the parentheses and apply the distributive property of multiplication to get,
⇒ 10√5 - 4√5√2
⇒ 10√5 - 4√(5 × 2)
⇒ 10√5 - 4√10
Therefore, the solution to the given expression is 10√5 - 4√10.
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The mass of an atom or molecule is measured in atomic mass units. Which is greater, a carat or a milligram?
Answers
Notice that:
[tex]\begin{gathered} -23<-21, \\ 8.3<10. \end{gathered}[/tex]Therefore:
[tex]8.3\times10^{-24}<10\times10^{-24}=10^{-23}<10^{-21}<1.66\times10^{-21}\text{.}[/tex]Then a carat is greater.
Now, since:
[tex]1atomic\text{ mass unit=8.3}\times10^{-24}carat.[/tex]Then:
[tex]\frac{1}{8.3}\times10^{24}\text{atomic mass unit=1carat.}[/tex]Simplifying the above result we get:
[tex]1\text{carat}=1.20\times10^{23}\text{atomic mass units.}[/tex]Also, since:
[tex]1\text{atomic mass unit=1.66}\times10^{-21}milligram[/tex]then:
[tex]\frac{1}{1.66}\times10^{21}\text{atomic mass unit=1 milligram.}[/tex]Simplifying the above result we get:
[tex]1\text{ milligram=6.02}\times10^{20}atomic\text{ mass units.}[/tex]Answer:
A carat is greater.
[tex]1\text{carat}=1.20\times10^{23}\text{atomic mass units.}[/tex]and
[tex]1\text{ milligram=6.02}\times10^{20}atomic\text{ mass units.}[/tex]and
The state transportation commission counted cars traveling east and west across a toll bridge. 75% of the 588 cars counted were traveling east. How many eastbound cars did the commission count?
Answers
Answer: the answer is 441
Step-by-step explanation: 75% of 588 is 441
what is the shape of a cross section that is perpendicular to the basis
Answers
If we get the cross section perpendicular to the base of this image, we would get the same shape as the image.
Through the diagram, we can see that if we cut the image to get the cross section perpendicular to its base, we would get the same shape as the image, which is a pentagon.
Question 2-20
Mrs. Kimsey purchased a bushel of large apples that weighs about 48 pounds. The bushel contains 96 apples. What is the approximate
weight, in ounces, of one apple?
02
O 16
32
Answers
Weight of one apple is 8 ounces.
We have to calculate the weight of one apple. For that firstly, we have to calculate the weight of one apple in pounds because we have been given the weight of 96 apples in pounds. After that, we will convert it into ounces and we know that one pound is equal to 16 ounces.
A bushel has 96 apples.
We have been given weight of 1 bushel which is 48 pounds.
Weight of 96 apples = 48 pounds
We have to calculate weight of one apple.
Weight of one apple = 48/96 = 1/2 pound
1 pound = 16 ounces.
Now, we have to convert pounds into ounces
Weight of one apple = 1/2 * 16 ounces
= 8 ounces
Hence, the answer is 8 ounces.
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The slope of like A is m=9 & the slope of line B is m-9. What is their relation?
O Parallel
O Perpendicular
O Neither
Answers
Find the percentage decrease and round to the nearest tenth
Answers
Answer:
16.6%
Step-by-step explanation:
First, find the difference between the prices:
$3.95 - $3.45 = $0.50
Then, divide the difference by yesterday's price.
$0.50 ÷ $3.95
≈ 0.166
≈ 16.6%
Answer:
12.7%
Step-by-step explanation:
$3.95 - $3.45 = $.50
$.50 / $3.95 = .127 = 12.7%
Ainsley had 3 yards of string. She used 1/4 yard for a project. She wants to divide the rest into pieces 5/6 yard long. How many pieces can she make?
Answers
She can make 3.3 pieces from the remaining length
How to determine the number of pieces to make?From the question, the given parameters are:
Length of string = 3 yardsAmount used for project = 1/4 yardLength of each piece = 5/6 yardWe start by calculating the length of the remaining pieces as a whole
This is calculated as
Length of remaining piece + length used for project = Length of string
Substitute the known values in the above equation
So, we have
Length of remaining piece + 1/4 yard = 3 yards
Subtract 1/4 from both sides
Length of remaining piece = 2.75 yards
The number of pieces is then calculated as
Pieces = Length of remaining pieces/Length of each piece
This gives
Pieces = 2.75 yards/(5/6 yards)
Evaluate the quotient
Pieces = 3.3
Hence, the number of pieces she can make is 3.3
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I need help with the question above. I took a picture of it.
Answers
The answer is: It will be a line.
given the preimage coordinates complete the translation provide and give the image Coordinates
Answers
The coordinates are made up of an x-coordinate and a y-coordinate, written in the form (x, y), the translation given is (x + 1, y - 1), which means adding +1 to all x-coordinates and subtracting -1 to all y-coordinate.
Then, the pair B(0, -4) will be transformed into B'(0 + 1, -4 - 1) → B'( 1, -5)
C( -1, 1) → C' (-1 + 1, 1 - 1) → C'( 0, 0)
D( 1, 3) → D' ( 1 + 1, 3 - 1) → D'( 2, 2)
E( 4, -1) → E' ( 4 + 1, -1 - 1) → E'( 5, -2)
please help and could u give all the steps if there’s more after this thank you so much
Answers
Angle IJL is 54 because congruent angles have equal measure.
What are congruent angles?
Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles.
According to question, angle m IKL = 54
And AB// CD and EF// GH
Angle IKL is alternate interior angle to angle HLK
m angle HLK= m angle IKL (congruent angles have equal measure)
m angle HLK= 54
Similarly, m angle IJL = m angle HLK
Hence, angle IJL= 54
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The half life of iron-59 is 44.5 days. How much of
a 50g sample would remain after 178 days?
Answers
Answer:
If the half-life of a nuclide is 44.5 days, then 178 days is four half-lives.
explanation:
After four half-lives, 0.0625 (0.54) of the original nuclides remains. If 50g is the original mass, then the mass after 4 half-lives is 3.125g.
AT = A0 2(-T/H)
A178 = (50) 2(-44.5/178)
A178 = 3.125
Which of the following would result in an integer?
O a.) 120
O b.) √144
O c.) √52
O d.) √24
Answers
The answer is either Option (a) or option(b) or both the options i.e, 120 or √144
What is Integer ?
An integer is a whole number from the set of -ve , non-negative , +ve and 0 numbers.
Let's see how both the option is correct
we know, integers are 0,1, 2, 3, .... or -1, -2 , -3 ......
Means the number which is not in fraction or decimal value or root.
so, by seeing option(a) we can say it's an integer
but in option(b) it's the root so how it is integer
The answer is simple it's perfect square of 12 so √144 = 12 so that means it have the value which is not in fraction. By that we can say that option(b) is also an integer
Now, in option(c) and (d) they are not the perfect square and their root results in decimal values. so we cannot tell them as an integer value.
Hence, the answer is either Option (a) or option(b) or both the options.
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Evaluate: base 6 exponent 0
Answers
Answer:
1
Explanation:
Given:
[tex]6^0[/tex]To evaluate the expression above, apply the law of indices below.
[tex]a^0=1,a\neq0[/tex]That is, whenever a number (except 0) is raised to the power of 0, the result is always 1.
Therefore:
[tex]6^0=1[/tex]2 5 4 Q Find the area of the shaded region above.
Answers
As you can see in the given figure, there are two different shapes.
One is a rectangle and the other is a triangle.
Recall that the area of a rectangle is given by
[tex]A_R=L\cdot W[/tex]Where L is the length and W is the width.
As you can see from the figure,
W = 4
L = 5
So the area of the rectangle is
[tex]A_R=L\cdot W=5\cdot4=20[/tex]Recall that the area of a triangle is given by
[tex]A_T=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base of the triangle and h is the height of the triangle.
As you can see from the figure,
b = 4
h = 2
So the area of the triangle is
[tex]A_T=\frac{1}{2}\cdot b\cdot h=\frac{1}{2}\cdot4\cdot2=\frac{1}{2}\cdot8=\frac{8}{2}=4[/tex]Now the total area of the shaded region is the sum of the area of the rectangle and the area of the triangle.
[tex]A=A_R+A_T=20+4=24[/tex]Therefore, the area of the shaded region is 24
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The formula for the area of a triangle is A = -bh, in which b represents the length of the base and h2represents the height. If a triangle has an area of 115 mm2 and the height is 10 mm, what is the measureof the base?The measure of the base ismm.
Answers
The formula for the area of a triangle is A is;
From 1982 to 2004, the number
B
of federally insured banks could be approximated by
B
(
t
)
=
−
326.6
t
+
13783
where t is the year and t=0 corresponds to 1982.
How many federally insured banks were there in 1987?
Find the slope of the graph of B.
Answers
There were 120150 federally insured bank in the year 1987. The slope of the graph of B is -326.6.
The provided function B(x) states the number of federally insured banks from 1982-2004.
The function B(x) is,
B(x) = -326.6t + 13783
Here t is representing the year,
This function is a linear function corresponding to an equation of line,
If according to the situation,
t = 0, signifies the year 1982,
Then the year 1983 should be represented by t = 1.
On continuing the pattern the year 1987 should be represented by t = 5.
So, the number of federally insured banks in year 1987 can be found by putting t = 5 in B(x),
B(5) = -326.6(5) + 13783
B(5) = 12150.
The number of banks federally insured in year 1987 is 12150.
The function is B(x)= -326.6t + 1783,
This is representing the point-slope form of the line,
y = mx + c,
On comparing the provided function with the standard equation we can see,
Slope m = -326.6
So the slope of the function is -326.6.
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Translate Pre image coordinates right 14 units and up 13 units.
Answers
We will have the following:
We translate the points:
A(-12, 3)
B(-6, -3)
C(-12, -9)
The transformation rule is (x, y) -> (x + 14, y + 13); so:
A'(2, 16)
B'(8, 10)
C'(2, 4)
1. A piece of power transmission equipment is being designed. The design includesa set of three different meshed gears with a total of 107 teeth between them. If thesecond gear has 13 more teeth than the first gear. The third gear has 15 more teeththan the second gear.How many teeth does the second gear have?
Answers
where x is the first, y the second and z the third
the second gear has 13 more teeth than the first gear
[tex]x+13=y[/tex]The third gear has 15 more teeth than the second gear
[tex]y+15=z[/tex]we need solve z form the third equation and solve x from the second equation an replace on the first
[tex]\begin{gathered} z=y+15 \\ x=y-13 \end{gathered}[/tex]replacing
[tex]\begin{gathered} (y-13)+y+(y+15)=107 \\ y-13+y+y+15=107 \\ 3y+2=107 \\ 3y=105 \\ y=35 \end{gathered}[/tex]so, the second gear have 35 teeth
I NEED HELP ASAP, I DONT KNOW HOW TO DO THIS.
Answers
Answer:
slope = 5/2
Step-by-step explanation:
Locations of points: (-4 , -4) and (-2 , 1)
slope = rise / run
between two plotted points this means that:
slope = change in y / change in x
slope = (1 - (-4)) / (-2 - (-4))
slope = 5/2
Solve and check the equation X-23=16
Answers
Answer:x=39
Step-by-step explanation:
x-23=16
x=16+23
x=39
Maria expandió el siguiente cuadrado (x+3)^2=x^2 Está correcta la forma que usò?
Answers
No, the form that Maria expanded is not correct.
What does it mean to "extend and simplify"?
We must multiply out the brackets in order to expand and simplify an expression, and we must then collect like words in order to simplify the resulting expression. We take out brackets by expanding them, often known as multiplying out.
Given:
(x+3)²
= x² + 2 . 3 . x + 3²
= x² + 6x + 9
Therefore the correct expansion is x² + 6x + 9.
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Question:
Maria expanded the following square (x+3)^2=x^2 Is the form she used correct?