Answers
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Label each row 1, 2, ..., all the way up to row 7. I'll refer to each statement and reason by the row number. For example, in row 2 we have "statement 2" and "reason 2". Statement 2 is already filled in for us while Reason 2 is blank.
Statement 1 has "CD perpendicular to AE". This is given to us to be true as shown in the "given" portion at the very top of the problem (just under the diagram).
What's also given to us is the fact that "line segment CD is parallel to line segment GH". So we'll write "given" for reason 2.
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Next up is reason 3, which is "definition of perpendicular". Why is this? Because the statement "angle ABD is a right angle" means angle ABD is 90 degrees. The term "perpendicular" means two lines or line segments or rays cross/meet at a 90 degree angle.
Now onto reason 5. Note how angle ABD and angle GEF are alternate exterior angles. They are outside of the train tracks (CD and GH) and lay on alternate sides of the line FA. Since CD is parallel to GH (see line 2), this means the alternate exterior angles are congruent. For reason 5, we'll put "alternate exterior angles theorem"
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Statement 7 is the the thing we want to prove. For any proof, the last statement is ALWAYS what you want to prove. If there's anything after this statement then we still have work to do and the proof isn't done. This is the last stop so to speak. So we simply write exactly what we want to prove (next to the "prove:" portion just below the diagram)
Reason 7 is "definition of perpendicular" because GEF is a right angle so GH is perpendicular to line FA. Like with reason 3, a 90 degree angle forms.
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Once again, check out the attached image to see all of the answers in the right spots.
Related Questions
Line GH contains points G(–2, 6) and H(5, –3). What is the slope of ?
Answers
We will use the slope formula and fill it in accordingly.
[tex] m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
Our x2 is 5 and x1 is -2; our y2 is -3 and y1 is 6
[tex] m=\frac{-3-6}{5-(-2)}=\frac{-9}{7} [/tex].
The slope of your line is -9/7
Answer
Find out the slope of the points G(–2, 6) and H(5, –3).
To prove
The equation for finding the slope of two points be
[tex]m = \frac{y_{2} -y_{1}}{x_{2} - x_{1}}[/tex]
where m represented the slope .
As given
points G(–2, 6) and H(5, –3).
[tex]m = \frac{-3-6}{5+2}[/tex]
solving the above terms
[tex]m = \frac{-9}{7}[/tex]
Therefore the slope of points G(–2, 6) and H(5, –3) is
[tex]m = \frac{-9}{7}[/tex]
Which expression is equivalent to 12x^4(x-3)(x+5)/ 30x(x+3)(x+5)
Answers
The equation which is equivalent to the given expression is 4x + y = 21.
What is an expression?Expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An expression is a combination of numbers, variables, or a combination of numbers and variables, and symbols and it is connected by the sign of equal.
We have,
Expression [tex]\frac{12x^4(x-3)(x+5)}{30x(x+3)(x+5)}[/tex]
So,
Now,
To get the equivalent expression,
Cancel the common factor (x + 5) of the given expression,
On solving,
We get,
[tex]\frac{12x^4(x-3)}{30x(x+3)}[/tex],
Now,
On solving further,
We get,
[tex]=\frac{2x^3(x-3)}{5(x+3)}[/tex]
So, We can not solve it further,
So, This is the expression that is equivalent to the given expression.
Hence, we can say that the equation which is equal to the given expression is [tex]\frac{2x^3(x-3)}{5(x+3)}[/tex].
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Write a compound inequality to represent all of the numbers between -4 and 6.
Answers
could also be : x > -4 and x < 6
Answer:-4 < x < 6
Step-by-step explanation:
Part of a tiling design is shown. The center is a regular hexagon. A square is on each side of the hexagon, and an equilateral triangle joins the squares. Complete the pattern around the hexagon and calculate the total area of the pattern.
A.
403.1 in.^2
B.
503.1 in.^2
C.
1,119.6 in.^2
D.
1,379.4 in.^2
Answers
There are 6 equilateral triangles around the hexagon, and the hexagon itself is made of 6 of those equilateral triangles. So 12× triangle's area will complete the total area.
Height of the triangle will split it into 2 30-60-90 triangles. So the h will be 5SR3, since the height will bisect the base (10) into 2 5's. And a 30-60-90 will have sides of x, xSR3, and 2x. Since x=5, the h will be 5SR3 = 8.66.
So area of the triangle:
1/2×b×h = 1/2×10×8.66 = 43.3
Now 12×43.3 = 519.62
Now add that to the 600 from the squares:
519.62 + 600 = 1,199.62 in^2
The correct answer is (C.)
Which expression is equivalent to the following complex fraction?
Answers
Which ordered pair is a solution of the inequality y>4x-5? A.(3,4) B.(2,1) C.(3,0) D.(1,1)
Answers
y>4x-5
1>4(1)-5
A student earned 37 out of 50 points on the last test. What percent correct did the student earn?
Answers
% correct = 37/50 * 100 = 74%
_____________________
% = percent = parts per 100 = x/ 100 ;
37/50 = x/100 ;
Looking at the denominators;
50 * (what value?) = 100 ?
→ 100 ÷ 50 = 2 ;
So; 50 * 2 = 100 ;
So; 37/50 = (37*2) / (50*2) = 74/100 = 74 % .
_______________________________________
The answer is: " 74% " .
_______________________________________
The programmer can type 55 words per minute.
At that rate, how many words can the programmer type in 11 min?
66
550
605
655
Answers
Answer:
605 words per 11 minutes!
Step-by-step explanation:
60 / 55 = 1.0909
11 x 60 = 660
660 / 1.0909 = 605 + (6x - [tex]\int\limits^a_c {b} \, dx[/tex]) / 10
605 + (6x - [tex]\int\limits^a_c {b} \, dx[/tex]) / 10 rounded = 605
Find the exact coordinates of the centroid for the region bounded by the curves y=x, y=1/x, y=0, and x=2
Answers
The centroid of the region bounded by [tex]\(y=x\), \(y=\frac{1}{x}\), \(y=0\),[/tex] and [tex]\(x=2\)[/tex] is at [tex]\((\frac{2}{3}, 0)\).[/tex]
To find the centroid of the region bounded by the curves[tex]\(y=x\), \(y=\frac{1}{x}\), \(y=0\), and \(x=2\),[/tex]we need to first find the area of the region and then compute the coordinates of the centroid using the following formulas:
The centroid of a region with area[tex]\(A\)[/tex] is given by [tex]\((\bar{x}, \bar{y})\)[/tex]where
[tex]\[\bar{x} = \frac{1}{A} \int\int_R x \, dA\][/tex]
[tex]\[\bar{y} = \frac{1}{A} \int\int_R y \, dA\][/tex]
First, let's find the points of intersection for the curves:
1. [tex]\(y=x\) and \(y=1/x\):[/tex]
[tex]\[ x = \frac{1}{x} \implies x^2 = 1 \implies x = 1 \][/tex]
So, the intersection point is [tex]\((1,1)\).[/tex]
2. [tex]\(y=0\) and \(x=2\):[/tex]
This intersection occurs at [tex]\((2,0)\).[/tex]
Now, we'll integrate to find the area and then the centroid:
1. Area:
[tex]\[ A = \int_{0}^{1} (x - \frac{1}{x}) \, dx + \int_{1}^{2} (\frac{1}{x}) \, dx \][/tex]
[tex]\[ A = \left[\frac{x^2}{2} - \ln|x|\right]_{0}^{1} + \left[\ln|x|\right]_{1}^{2} \][/tex]
[tex]\[ A = \left(\frac{1}{2} - 0 - (0 - \infty)\right) + (\ln(2) - \ln(1)) \][/tex]
[tex]\[ A = \frac{1}{2} + \ln(2) \][/tex]
2. Centroid[tex](\(\bar{x}\)):[/tex]
[tex]\[ \bar{x} = \frac{1}{A} \left[\int_{0}^{1} x(x - \frac{1}{x}) \, dx + \int_{1}^{2} x(\frac{1}{x}) \, dx\right] \][/tex]
[tex]\[ \bar{x} = \frac{1}{A} \left[\left[\frac{x^3}{3} - \frac{1}{2}\ln|x|\right]_{0}^{1} + \left[\ln|x|\right]_{1}^{2}\right] \][/tex]
[tex]\[ \bar{x} = \frac{1}{A} \left(\frac{1}{3} - 0 - (0 - \infty) + (\ln(2) - \ln(1))\right) \][/tex]
[tex]\[ \bar{x} = \frac{\frac{1}{3} + \ln(2)}{\frac{1}{2} + \ln(2)} \][/tex]
[tex]\[ \bar{x} = \frac{2}{3} \][/tex]
3. Centroid [tex](\(\bar{y}\)):[/tex]
[tex]\[ \bar{y} = \frac{1}{A} \left[\int_{0}^{1} (x - \frac{1}{x}) \cdot 0 \, dx + \int_{1}^{2} (\frac{1}{x}) \cdot 0 \, dx\right] \][/tex]
[tex]\[ \bar{y} = 0 \][/tex]
Therefore, the centroid of the region is at the point [tex]\(\left(\frac{2}{3}, 0\right)\).[/tex]
What is the slope of the line passing through the points (6, 7) and (1, 5) ?
Answers
y=2/5x and then your y-intercept
If a line has a positive slope what is its general direction
Answers
A line with a positive slope generally moves upward from left to right, representing an increase in y-values as x-values rise.
Explanation:If a line has a positive slope, its general direction is upward from left to right. This means that as the x-values increase, the y-values also increase. The slope of a line in mathematics represents the rate at which y changes with respect to x. A positive slope indicates a direct relationship between the two variables involved; as one increases, so does the other. In the context of a graph, this manifests as a line that rises as it moves along the x-axis.
The nature of the slope determines the line's direction. A higher positive slope indicates a steeper ascent, while a smaller positive slope results in a less steep, flatter incline. The concept of slope is crucial in economics as well, as it measures the relationship between two variables, such as price and quantity supplied, where a positive slope illustrates that firms supply more as the price goes higher.
All of the items in a bicycle shop are on sale for 30% off the regular price. Rene spends $74.90 to buy a bicycle and a helmet (without taxes). If the regular price of the bicycle is $85, which equation can be used to find the regular price of the helmet, h?
Answers
x= helmet
Equation to find the helmet price;
x = 74.90 - [85 - (30/100 *85)]
If you want the price helmet
x = 15.40
Answer:
0.7 (85 + h) = 74.90
Step-by-step explanation:
A publisher claims that the average salary paid at its company is $37,500 but it could differ as much as $4,500. Write and solve an absolute value inequality to determine the range of salaries at this company.
|x − 37500| ≤ 4500; The salaries range from $33,000 to $42,000
|x − 37,500| ≤ 4500; The salaries are less than $33,000 or greater than $42,000.
|x − 37500| ≥ 4500; The salaries range from $33,000 to $42,000
|x − 37,500| ≥ 4500; The salaries are less than $33,000 or greater than $42,000.
Answers
Which expression will produce a positive product:
(-12)(12)(-6.3)(-0.2)(-15.9)
(12)(-6.3)(-0.2)(-15.9
(-12)(12)(-6.3)(-0.2)(-15.9)(0)
(12)(12)(6.3)(0.2)(-15.9)
Answers
Final answer:
To produce a positive product, the expression (12)(-6.3)(-0.2)(-15.9) should be used.
Explanation:
To determine which expression will produce a positive product, we need to consider the sign rules for multiplication.
If we have an even number of negative signs within a set of parentheses, the product will be positive. If we have an odd number of negative signs, the product will be negative.
Let's analyze the given expressions:
(-12)(12)(-6.3)(-0.2)(-15.9): This expression has five negative signs, which means it will produce a negative product.(12)(-6.3)(-0.2)(-15.9): This expression has four negative signs, which means it will produce a positive product.(-12)(12)(-6.3)(-0.2)(-15.9)(0): This expression includes a 0, and any product multiplied by 0 will be 0, which is neither positive nor negative.(12)(12)(6.3)(0.2)(-15.9): This expression has one negative sign, which means it will produce a negative product.Therefore, the expression (12)(-6.3)(-0.2)(-15.9) will produce a positive product.
The expression that will produce a positive product is (12)(-6.3)(-0.2)(-15.9) because it contains an even number of negative signs, which results in a positive product according to the rules of multiplication regarding signs.
Explanation:To find which expression will produce a positive product, we must recall the rules of multiplication regarding signs:
When two positive numbers multiply, the result is positive (e.g., 2x3 = 6).When two negative numbers multiply, the result is also positive (e.g., (-4) x (-3) = 12).When multiply numbers with opposite signs, the result is negative (e.g., (-3) x 2 = -6 and 4 x (-4) = -16).When any number is multiplied by zero, the result is always zero.We can now evaluate the expressions given:
(-12)(12)(-6.3)(-0.2)(-15.9): This expression has an odd number of negative signs, so the product is negative.(12)(-6.3)(-0.2)(-15.9): This has an even number of negative signs, making the product positive.(-12)(12)(-6.3)(-0.2)(-15.9)(0): The presence of a zero means the product is zero.(12)(12)(6.3)(0.2)(-15.9): This has one negative sign, so the product is negative.The correct expression that will produce a positive product is (12)(-6.3)(-0.2)(-15.9).
A regulation baseball field measures 90 feet between each base. What is the distance around the bases in yards?
Answers
1st base to 2nd base = 90 ft
2nd base to 3rd base = 90 ft
3rd base to home = 90 ft
so we have a total of : (90 * 4) = 360 ft
there are 3 ft in 1 yd....
so in 360 ft, there are : 360/3 = 120 yds <==
or u could just figure it between each base....90 ft = (90/3) = 30 yds per base...and u have 4 bases....so that (4 * 30) = 120 yds
The distance around the bases in yards is 30 yards.
In order to determine the distance between each base in yards the unit of conversion of feet to yards have to be first determined. 1 foot is equivalent to 0.333333 yards.
1 feet = 0.333333 yards
The second step is to multiply the distance between each base by the unit of conversion.
Distance between each base x unit of conversion
90 x 0.333333
= 30 yards
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please help for the first two questions! i don't know how to do them.
Answers
write the expression in standard form. 3/3-12i
Answers
and you want complex form as in a+bi
remember that [tex]i=\sqrt{-1}[/tex] so [tex]i^2=-1[/tex]
and remember conguates
we don't want imaginary numbers in the denomenator so
first sipmlify the farction
[tex]\frac{1}{1-4i}[/tex]
multiply it by [tex]\frac{1+4i}{1+4i}[/tex]
result is
[tex]\frac{1+4i}{(1)^2-(4i)^2}[/tex]
[tex]\frac{1+4i}{1-16i^2}[/tex]
[tex]\frac{1+4i}{1-16(-1)}[/tex]
[tex]\frac{1+4i}{1+16}[/tex]
[tex]\frac{1+4i}{17}[/tex]
[tex]\frac{1}{17}+\frac{4i}{17}[/tex]
in standard form (a+bi form) [tex]\frac{3}{3-12i}[/tex] is
[tex]\frac{1}{17}+\frac{4}{17}i[/tex]
The expression '3/3 - 12i' simplifies to '1 - 12i' which is already in the standard form for a complex number.
Explanation:The expression you've mentioned is 3/3-12i. First, we need to simplify it. The term 3/3 equals to 1. So, the expression becomes 1 - 12i. This is already in a standard form for a complex number.Standard form for a complex number is represented as a + bi, where a and b are real numbers and i represents the imaginary unit. Therefore, our expression 1-12i is in standard form of complex numbers, where a=1 (real part) and b=-12 (imaginary part).
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which of the following answer choices describes all the transformation found in the cubic function f(x)=-(x+2)3-5
Answers
You need to perform three transformations to the cubic function to obtain
f(x) = - (x + 2)^3 - 5.
Those transfformations are:
1) Shift f(x) = x^3, 2 units leftward to obtain f(x) = (x + 2)^3
2) reflect f(x) = (x + 2)^3 across the x-axis to obtain f(x) = - (x + 2)^3
3) shift f(x) = - ( x + 2) ^3, 5 units downward to obtain f(x) = - (x + 2)^3 - 5
Circle the step where the error has occurred. Explain why it is an error.
Given: 2(10−13)=−34+60
Step 1: Distribute
20−26 = −34+60
Step 2: Addition Property of Equality
−26 = −34+80
Step 3: Addition Property of Equality
8=80
Step 4: Division Property of Equality
=10
Answers
20 - 26 = -34 + 60 (distribute)...correct
-26 = -34 + 40 <=== here it is....he added 20 instead of subtracting 20...he should have used the subtraction property
Answer:
error in step 2. 20 is added on both sides instead of subtraction.
Step-by-step explanation:
Given: [tex]2(10-13)=-34+60[/tex]
Step 1: Distribute
[tex]20-26 = -34+60[/tex]
2 is distributed inside the parenthesis. 2 times 10 is 20
2 times -13 is -26
Step 2: Addition Property of Equality
[tex]-26 = -34+80[/tex]
To eliminate 20 we subtract 20 from both sides. Here 20 is added on both sides. To eliminate any number we do opposite operation. So there is an error in this step.
Step 3: Addition Property of Equality
8=80
Step 4: Division Property of Equality
=10
What is the GCF of 15 and 27 ?
Answers
If f(x) =3x^2 and g(x) =4x^3 +1 what is the degree of fg (x)
Answers
Now, when you expand the bracket, you will find that the highest degree or degree of the polynomial is 6.
∴degree of fg (x) = 6
Matt has a block. He uses one of the flat surfaces of the block to trace a triangle. What type of solid figure is Matt's block?
Answers
The types of 3D objects on which one face is triangular are triangular prism, triangular-based pyramid, and square-based pyramid so Matt's solid figure can be anyone among the three.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
As per the given,
Matt used a 3D block to draw a triangle on the paper.
Now in order to draw a triangle there are three types of 3D objects that can be used,
01) Triangular prism,
02) Triangular-based pyramid
03) Square-based pyramid
Hence "The types of 3D objects on which one face is triangular are triangular prism, triangular-based pyramid, and square-based pyramid so Matt's solid figure can be anyone among the three".
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Assume that the salaries of elementary school teachers in the united states are normally distributed with a mean of $26,000 and a standard deviation of $5000. what is the cutoff salary for teachers in the bottom 10%?
Answers
True or false any number in the form of a + bi where a and b are real numbers
Answers
True........................
Foster is centering a photo that is 1/1 2 inches wide on a scrapbook page that is 10 inches wide. How far from each side of the page should he put the picture? Please enter it as a mixed number
I will give 39 points if you answer this question
Answers
10-1.5=8.5/2=4.25
Hope this helps!
Can u plz mark me as brainliest? I really need it!
Answer: 4.25
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!
How many solutions does the equation have?
2x+3+4x x2
A)many solutions
B)no solutions
C)1 solution
Answers
Solve:C=10d + 5n for n
Answers
[tex]n = - 2d + \frac{c}{5} [/tex]
hope this helps
can u please give me an answer best gets the brainliest
Answers
Can Anyone Help Me
The number of e-mails sent each day in the United States is measured in the thousands.
A. True
B. False
Answers
Mrs evans has 120 crayons and 30 pieces of paper to give to her students. what is the largest number of students she can have so that each student gets equal number of crayons and equal number of pieces of paper
Answers
The maximum number of students that will receive the paper and crayons are 30.
What is ratio?
Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
Given is Mrs. Evans who has 120 crayons and 30 pieces of paper to give to her students.
We have 120 crayons and 30 pieces of paper.
Then for 1 paper, we will have (120/30) which is equivalent to 4 crayons.
So, every student will get 1 paper and 4 crayons.
Assume that the maximum number of students that will receive the paper and crayons are [x]. Then, we can write -
x + 4x = 120 + 30
5x = 150
5x = 150
x = 30
Therefore, the maximum number of students that will receive the paper and crayons are 30.
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