30 = m<1 = m<2
m<1 is equals to m<2 because these two angles are transitive property.
How to identify the correct justification for m<1 = 30° and m<2 = 30°?given that m<1 = 30° and m<2 = 30°.
m<1 = 30
m<2 equals to m<1
m<2 = 30 can be obtained by substituting 30 into the second equation.
The proof is now complete.
The Transitive Property of Equality can also be used, which asserts that if X = Y and Y = Z, then X = Y = Z. In other words, if one number is equal to another, and that other number is equal to a third, then all three numbers must be the same.
thus, 30 = m<1 = m<2, m<1 is equals to m<2 because these two angles are transitive property.
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At the end of spring break, Mary left the beach and drove back towards home, driving at a rate of 51 mph. A friend of Mary left the beach for home 0.5 hour later, and drove 66 mph. How long did it take Mary's friend to catch up to Mary?
Answer:
2.2 hours or
2 hours and 12 minutes they will meet.
Step-by-step explanation:
Givens
Mary's speed = 51 mph
Friend's speed = 66 mph
Mary will be on the road for t hours
Her Friend will be on the road t - 0.5. Why minus? Because she was on the road 1/2 hour less than Mary was. Any time you see More or Less in a question, pay attention. usually it is the key to the question.
Equation
d_Mary = d_friend
d = rate * time
Solution
51 * t = 66*(t - 0.5) Remove the brackets.
51*t = 66*t - 66*0.5
51*t = 66*t - 33 Subtract 66t from both sides. Be careful
51t - 66t = - 33 Combine
- 15t = - 33 Divide by - 15
t = - 33/-15
t = 2.2 hours or 2 hours and 12 minutues
The lengths of the four sides of a quadrilateral (in meters) are consecutive integers. If the perimeter is 42 meters, find the value of the longest of the four side lengths.
The four sides of the quadrilateral are 9 m,10 m, 11 m and 12 m.
What is a quadrilateral?
A quadrilateral is a four-sided polygon with four angles and four vertices. The term "quadrilateral" comes from the Latin words "quadri," which means "four," and "latus," which means "side."
Let the four sides of the quadrilateral be (x-2), (x-1), x, (x+1).
Then, perimeter = (x-2) + (x-1) + x + (x+1)
i.e., x - 2 + x - 1 + x + x + 1 = 42
i.e., 4x - 2 = 42
i.e., 4x = 42 + 2
i.e., 4x = 44
i.e., x = 11
Hence, the four sides of the quadrilateral are 9 meters, 10 meters, 11 meters and 12 meters.
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-4x + y = 5. Solve for y
A. y = -4x + 5
B.y = 4x + 5
C. y = 4x - 5
D. y = -4x - 5
Answer:
y = 4x + 5
Step-by-step explanation:
-4x + y = 5
-4x + 4x + y = 5 + 4x
y = 5 + 4x
Hope this helps! :)
If the two lines below are perpendicular and the slope of the red line is -,
what is the slope of the green line?
-5
01
A
5
5
We get that the slope of the green line will be 2 / 5 when it is perpendicular to the red line.
We are given that the red line is perpendicular to the green line.
Also, we are given that the slope of the red line is - 5 / 2
m₁ = - 5 / 2
Now, we need to find the slope of green line.
Let the slope of the green line be m₂
We know that, when the lines are perpendicular, then the relationship between their slopes is given by:
m₁ × m₂ = - 1
Substituting the values, we get that:
- 5 / 2 × m₂ = - 1
m₂ = - 1 × - 2 / 5
m₂ = 2 / 5
Therefore, we get that the slope of the green line will be 2 / 5 when it is perpendicular to the red line.
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In the figure below, points Y, S, R, and Q lie in plane P.
Points T and X do not lie in plane P.
For each part below, fill in the blanks to write a true statement.
P
R
S
P
(a) S, , and
(b) TX and 0
are distinct points that are collinear.
are distinct lines that intersect.
(c) Point Y and line are coplanar.
(d) Another name for plane P is plane
a. S, R, and Q are distinct points that are collinear.
b. TX and QS are distinct lines that intersect.
c. Point Y and line QS are coplanar.
d. Another name for plane P is: plane QSY.
What are Colinear Points?Points that lie on the same straight line are collinear points.
What are Coplanar Lines?If two lines are lie on the same plane, they are referred to as coplanar lines.
a. S, R, and Q are on a straight line. Therefore:
S, R, and Q are distinct points that are collinear.
b. TX and QS are distinct lines that intersect.
c. Point Y and line QS are on the same plane. Therefore:
Point Y and line QS are coplanar.
d. Another name for plane P is: plane QSY.
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Complete the statement 7 divide by blank
=56
Based on the statement given, the completion of the statement is 7 divided by 1/8 = 56.
What divides 7 to give 56?The statement is asking for the number that would divide 7 such that the result of this division would be 56.
Assuming the number is x, the formula would be:
7/x = 56
Here, x would be the mystery number that would divide 7 to give 56.
Solving for x is:
7/x = 56
7 = 56x
x = 7/ 56
x = 1/8
In conclusion, when 7 is divided by 1/8, it gives 56.
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a bakery has six bags of flour. they are are asked to make four loaves of bread
the first two loaves each require two bags and quarter of another bag
the next loaf requires one bag and two thirds of another bag
the final loaf requires a half bags of flour
write a calculation,using brackets ,to work out how much flour the bakery will have left the bakery will have left after making these loaves
The bakery is short on half a bag of flour.This problem can be solved using fractions . So, first loaf of bread requires 2bags of flour and a quarter which can be written as 2[tex]\frac{1}{4}[/tex]second loaf of bread also requires the same amount which is 2[tex]\frac{1}{4}[/tex]
the third loaf of bread requires one bag and two third of another bag which can be written as 1[tex]\frac{2}{3}[/tex]
And the final loaf of bread requires half bag of flour which is [tex]\frac{1}{2}[/tex]
the total requirement of flour for making the four loaves of bread is
= 2[tex]\frac{1}{4}[/tex] + 2[tex]\frac{1}{4}[/tex]+ 1[tex]\frac{2}{3}[/tex]+[tex]\frac{1}{2}[/tex]
=[tex]\frac{9}{4}[/tex] +[tex]\frac{9}{4}[/tex] + [tex]\frac{5}{3}[/tex] + [tex]\frac{1}{2}[/tex]
= [tex]\frac{27}{12}[/tex]+ [tex]\frac{27}{12}[/tex] +[tex]\frac{20}{12}[/tex] +[tex]\frac{6}{12}[/tex]
= [tex]\frac{80}{12}[/tex]
To work out how much flour the bakery will have left after making these loaves we need to reduce the total requirement with total flour we have = 6 -[tex]\frac{80}{12}[/tex]
=[tex]\frac{72}{12}[/tex] - [tex]\frac{80}{12}[/tex]
=- [tex]\frac{6}{12}[/tex] or- [tex]\frac{1}{2}[/tex]
therefore the bakery is short on half a bag of flour
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2. The coordinates of the vertices of quadrilateral ABCD are A(-6,-1), B(-5,2), C(-1.-5), and D(0.-2).
Parker states that quadrilateral ABCD is a parallelogram. Prove or disprove Parker's statement.
The given quadrilateral is not a parallelogram.
According to the statement
We have to find that the whether the quadrilateral is a parallelogram or not.
So, For this purpose, we know that the
A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
From the given information:
The coordinates of the vertices of quadrilateral ABCD are A(-6,-1), B(-5,2), C(-1.-5), and D(0.-2).
Then
To show that the diagonals are bisect each other, we have to find the midpoint of both diagonals and if the midpoint is same then they bisect each other.
So,
Midpoint of AC = Midpoint of BD
Midpoint of A(-6,-1),C(-1.-5) = Midpoint of B(-5,2),D(0.-2)
( -6-1/2 , -1-5/2) = (-5+0/2 , 2-2/0)
( -7/2 , -6/2) = (-5/2 , 0/2)
And these midpoints are not same then they do not bisect each other and then it is not a parallelogram.
So, The given quadrilateral is not a parallelogram.
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Polygon ABCDE is reflected across the
line x = -2. Graph and label the image
A'B'C'D'E'. Is mLA = mLA'? Explain.
The labeled graph showing ABCDE, A'B'C'D'E', and the line of reflection x = -2 is shown. Also, m∠ A = m∠ A'.
In the question, we are given that the polygon ABCDE is reflected across the line x = - 2.
We are asked to graph and label the image A'B'C'D'E'. Also, we are asked if m∠ A = m∠ A'.
When the polygon ABCDE is reflected across the line x = - 2, all the coordinates on it are reflected across the line x = -2.
The reflection of any point with coordinates (x, y) on reflection across the line x = a, results in a point with coordinates (-x + 2a, y).
The coordinates of the vertices of the given polygon are:
A (-4, 4), B (-3, 3), C (-3, 2), D (-5, 1), and E (-5, 3).
Reflecting these points across the line x = - 2, we get:
A (-4, 4) → A' ( -(-4) + 2(-2), 4) = A' (0, 4).
B (-3, 3) → B' ( -(-3) + 2(-2), 3) = B' (-1, 3).
C (-3, 2) → C' ( -(-3) + 2(-2), 2) = C' (-1, 2).
D ( -5, 1) → D' ( -(-5) + 2(-2), 1) = D' (1, 1).
E (-5, 3) → E' ( -(-5) + 2(-2), 3) = E' (1, 3).
Plotting ABCDE, A'B'C'D'E', and the line x = -2 has been shown on the graph.
The angles m∠ A and m∠ A' are equal since ABCDE is reflected to make A'B'C'D'E' which makes the two figures congruent. And in congruent figures, the corresponding angles are equal.
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Determine the domain of the following graph:
Answer:
[-10, 2]
Step-by-step explanation:
The domain is the set of x values.
Identify as an increase or decrease. Then find the percent of increase or decrease. If necessary, round to the nearest tenth of a percent. Original: 90 New: 160
Answer:
Since the quantity started at 90 and then changed to 160, there was clearly an increase in its value.
Step-by-step explanation:
Pls help
Solve for y.
–4|y| − 1 = –13
Answer:
3
Step-by-step explanation:
-4|3| -1 = -13
-12 -1 = -13
-13 = -13
Answer:
3
Step-by-step explanation:
-4|3| -1 = -13
-12 -1 = -13
-13 = -13
Triangle ABC is shown on the grid.
What is the perimeter of triangle ABC?
9 + units
9 + units
9 + units
9 + units
(C) The perimeter of the ΔABC is 9 + √41 units.
A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter.
The vertices of the triangle on the girds are A( - 1, 5 ), B( 4, 5 ), and C( - 1, 1 ).
The distance formula for the length of a line segment is given as:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore,
[tex]AB=\sqrt{(4-(-1))^2+(5-5)^2}=\sqrt{(4+1)^2+0}=5[/tex]
[tex]BC=\sqrt{(-1-4)^2+(1-5)^2}=\sqrt{(-5)^2+(-4)^2}=\sqrt{25+16}\\BC=\sqrt{41}[/tex]
[tex]AC=\sqrt{(-1-(-1))^2+(1-5)^2}=\sqrt{(-1+1)^2+(-4)^2}\\AC=\sqrt{0+16}=4[/tex]
Hence, the length of the sides of the triangle are [tex]5,\sqrt{41},4[/tex] units.
Now, the perimeter of a triangle is the sum of all three sides of the triangle.
Therefore, the perimeter of the triangle ABC is:
P = AB + BC + AC
P = 5 + √41 + 4
P = 9 + √41 units
Therefore, the perimeter of ABC is 9 + √41 units.
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The complete question is mentioned below:
Triangle ABC is shown on the grid.
What is the perimeter of triangle ABC?
(A) 9 + √21 units
(B) 9 + √29 units
(C) 9 + √41 units
(D) 9 + √61 units
partial products
16x29?
Step-by-step explanation:
464
first u will multiply 16 with 29
after u get that number that will be your answer
Answer:
29
× 16
54
120
90
+ 200
= 464
Use the equation y=5/2 x to complete the table. What is the value of A?
we need the table to answer the question
Which of the following are the most likely factors of the function
graphed above?
O(x+1)(x-5)
0 (x)(x-5)
0 (x-1)(x+5)
0 (x)(x+5)
2. Suppose a parabola has an axis of symmetry at x = -8, a maximum height of 2, and passes
Answer:3
Step-by-step explanation:bc
Marcellus's lawn is 4/5 of an acre. If 10 1/2 pounds of fertilizer are needed for 2 acres, how many pounds will he need to fertilize his lawn.
Based on the area of Marcellus's lawn, the number of pounds of fertilizer needed for Marcellus's lawn is 4 ¹/₅ pounds
How much fertilizer is needed?In order to fertilize an area of 2 acres, the number of pounds of fertilizer needed is 10 ¹/₂ pounds.
The area of Marcellus's lawn is only 4/5 of an acre however so to find the pounds of fertilizer needed, use direct proportion:
2 acres : 10 ¹/₂ pounds
4/5 acres : x
2x = 8.4
x = 8.4 / 2
x = 4.2 pounds
= 4 ¹/₅ pounds
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whats the answer for?(9.6x103)x(6.7x102)
Answer:
675,745.92
Step-by-step explanation:
(9.6 × 103) × (6.7 × 102)
(988.8) × (683.4)
= 675,745.92
I hope this helps!
if fx(x)=3x -1 and g(x)x^2 then what is (fog)(x)
The result function of (fog)(x) in the given functions is 3x² - 1.
What is the result function of (fog)(x)?Given the functions in the questions;
fx(x) = 3x - 1g(x) = x²(fog)(x) = ?Set up the composite result function and simplify.
(fog)(x) = f(g(x) = f(x²)
Evaluate f(x²) by substituting in the value of g into f
fx(x) = 3x - 1
f(x²) = 3(x²) - 1
Now, simplify
f(x²) = 3(x²) - 1
f(x²) = 3x² - 1
Therefore the result function of (fog)(x) in the given functions is 3x² - 1.
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There are three sections of College Algebra at Stellar
University. Section B has twice as many students as section A
has. Section C is has greater than or equal to the number of
students enrolled in section A plus B.
If there are 24 students in section C, what is the maximum
number of students that could be in section A?
Answer:
8 students
c>=A+B
b=2a
24<=C
The average (or mean) annual rainfall for Bramford, Ohio is 51 inches, and the rainfall for last year was 29 inches. What is the change in rainfall between the rainfall last year and the average (or mean) annual rainfall?
The change in rainfall between the rainfall last year and the average (or mean) annual rainfall is 22 inches
What is the change in rainfall between the rainfall last year and the average (or mean) annual rainfall?The given parameters are
Average annual rainfall = 51 inches
Last year = 29 inches
The change in rainfall between the rainfall last year and the average (or mean) annual rainfall is calculated as
Change = |Annual rainfall - Last year|
This gives
Change = |51 - 29|
Evaluate
Change = 22
Hence, the change in rainfall between the rainfall last year and the average (or mean) annual rainfall is 22 inches
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Solve the system of linear equations by graphing.
By using a graphing tool, the point of intersection of the two lines is (x, y) = (7, 0).
How to solve a system of linear equations by graphic approach
In this question we have a system of two linear equations with two variables, which can be represented on Cartesian plane. By geometry it is known that a line can be constructed after knowing the location of two distinct points.
First, we find two distinct points from each line:
x + y = 7: (7, 0), (0, 7)
- x + y = - 7: (7, 0), (0, - 7)
Second, set each pair of points and construct the lines on a Cartesian plane.
Third, mark the point of intersection of the two lines. The result is shown in the image attached aside. The point of intersection of the two lines is (x, y) = (7, 0).
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The diameter of a gold atom is approximately 144 trillionths of a metre. The diameter of an oxygen atom is approximately 0.074 billionths of a metre. Which is larger? How many times larger is it than the other?
The diameter of the gold atom is greater than the diameter of the oxygen atom by 7 x 10^-11 meter
What is a diameter?The diameter of a shape (usually a round shape) is a line that divides the shape to equal parts
Which is larger?The diameters are given as:
Diameter of a gold atom = approximately 144 trillionths of a meter
Diameter of an oxygen atom = approximately 0.074 billionths meter
Using a calculator, we convert the above numbers to scientific numbers
So, we have
Diameter of a gold atom = approximately 1.44 x 10^-10 meter
Diameter of an oxygen atom = approximately 7.4 x 10^-11 meter
The number with the higher exponent is greater than the other number
Hence, the diameter of the gold atom is greater than the diameter of the oxygen atom
How many times larger is it than the other?In (a), we have
Diameter of a gold atom = approximately 1.44 x 10^-10 meter
Diameter of an oxygen atom = approximately 7.4 x 10^-11 meter
Calculate the difference
d = 1.44 x 10^-10 - 7.4 x 10^-11
Evaluate the difference
d = 7 x 10^-11
Hence, the diameter of the gold atom is greater than the diameter of the oxygen atom by 7 x 10^-11 meter
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rectangle PQRS with vertices (5,15) Q(15,15) R(15,10) and S(5,10): k=4/5
The vertices of the rectangle are:
P'(4,12)
Q'(12,12)
R'(12,8)
S'(4,8)
Given,the vertices of the rectangle are:
P(5,15), Q(15,15), R(15,10) and S(5,10)
also k= 4/5 to find the new vertices, that is:
P' = P×k
P' = P × 4/5
P' = (5×4/5 , 15×4/5)
P' = (4,12)
similarly:
Q' = Q×k
Q' = Q × 4/5
Q' = (15×4/5 , 15×4/5)
Q' = (12,12)
R' = R×k
R' = R × 4/5
R' = (15×4/5 , 10×4/5)
R' = (12,8)
S' = S×k
S' = S × 4/5
S' = (5×4/5 , 10×4/5)
S' = (4,8)
Hence we get the required points, for which we plot the graph.
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Represent the following sentence as an algebraic expression, where "a number" is the letter x. 3 is decreased by a number.
Answer:
3-x
Step-by-step explanation:
A supermarket wants to send code for $.25 off a bag of chips to its rewards members. Each coupon will have one digit followed by four letters the letters D and E, and the digits 0, 5and 8 will not be used so there are 24 letters and 7 digits that will be used assume that the letters can be repeated how many such coupons can be generated.
There are 2322432 coupons generated .
According to the question we have been given that the code contains one digit followed by four letters . That is it can be assumed as
code = D L L L L where D and L represent the digits and letters.
Now total digits we have is = 7
total number of letters we have = 24
So we have to choose the first digit from these 7 digits. Thus there are 7 ways in which we can choose as they are repeated.
Also there are 24 ways to select the 4 letters after the digits as the letters are being repeated, that is ways = 24⁴
Therefore the number of coupons that can be generated from the combination are :
7*24⁴ = 7*331776
= 2322432
Hence the number of coupons generated are 2322432.
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The points I, J, K and L all lie on the same line segment, in that order, such that the ratio IJ:JK:KL is equal to 2:5:5 IfIL=60, find KL.
By definitions of collinearity and line segment, the length of the line segment KL is equal to 25 units.
What is the length of a line segment within another line segment?
In this problem we find four points that are collinear, that is, that lie in the same line. Therefore, there are three consecutive line segments: IJ, JK and KL, whose ratios are known. From the statement, we derive the following formula for KL:
KL = (5 / 12) · IL
KL = (5 / 12) · 60
KL = 25
The length of the line segment KL is equal to 25 units.
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(√14 + √10i)(√14 - √10i)
Answer:
24
Step-by-step explanation:
You want the value of the product ...
(√14 + √10i)(√14 - √10i)
Difference of squaresThe factoring of the difference of squares is ...
a² -b² = (a +b)(a -b)
Here, we have a=√14 and b=√10i. The product of the sum and difference of these values is ...
(√14 + √10i)(√14 - √10i) = (√14)² -(√10i)²
= 14 -(10(-1)) = 24
The product is 24.
Find the equation of the line using the given information. The slope is undefined and it passes through the point (x, y) = (8, 6).
Answer:
x= 8
Step-by-step explanation:
Vertical lines have undefined slopes, with an equation of x= ____. This is because when using the slope formula, the denominator would be a zero. The coordinates of points that lie on a vertical line have the same y-coordinate, but different x-coordinate value.
Given that the line passes through (8, 6), the line has an equation of x= 8.
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A bookstore manager purchased a case of
40 paperback books and a display stand
that cost $8.00. He paid $108.00 for the
total purchase. If each book cost the same
amount, how much did he pay per book?
A
B
C
D
$0.34
$2.50
$2.70
$100.00
