∠2 is congruent to ∠6 based on corresponding angle theorem.
What is corresponding angle theorem?Corresponding angles are formed when two parallel lines are intersected by a transversal line.The corresponding angles theorem states that "when a line intersects two parallel lines, the corresponding angles in the two regions of intersection are congruent."Assume that A, B, and C are distinct lines. Then A and B are parallel if and only if the corresponding angles of intersection of A and C, as well as B and Care, are equal.So here ,
Since in this question they are corresponding angles of parallel lines cut by a transversal, they are ∠2 ≅ ∠6 according to the Vertical Angles Theorem.
The complete question is : "Lines c and d are parallel lines cut by transversal p. Horizontal and parallel lines c and d are cut by transversal p. On line c where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 1, 2, 3, 4. On line d where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 5, 6, 7, 8. Which must be true by the corresponding angles theorem?"
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State the theorem that proves the triangles are congruent. Then write a congruence statement.
These two triangles are congruent by angle angle side(AAS) congruency theorem.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
From the given figure line segment AB is similar to line segment CD.
Angle E is congruent to angle D hence line segment AB is congruent to line segment BC.
So, These two triangles are congruent by angle angle side congruency theorem.
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!What is the range of temperatures in the data STEM AND LEAF!
Help solve number 16 of a proof please
1. Given
2. Alternate interior angles theorem
3. Given
4. Vertical angles
5. ASA
Mr. Bean puts $5000 in a mutual
fund that increases in value by 11% each
year. How many years will it take him to
reach $23,000 in his mutual fund?
Answer:
It's going to take 32.7 years
Could you guys also show how you got it? Thanks!
After solving the linear equation in two variables we get the value of x=13 and y =-24/5
What is linear equation in two variable?
If an equation is written in the form axe + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables.
Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.
Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalizes the two sides of the equation.
A system of linear equations in two variables can be solved using one of five techniques. These techniques are described below:
Method of GraphicalMethod of Cross Multiplication, Cross Multiplication MethodElimination MethodDeterminant Method2x+5y=2 multiply this equation by 2
we get,
4x+10y=4
And the other equation is :-
5x+10y=17
Subtracting both the equation we get :-
4x+10y=4
5x+10y=17
- - -
________
-x =-13
x=13
y=2-26/5
y=-4.8 or -24/5
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12 divided by 127 show your work
Answer:
10.58
Step-by-step explanation:
23. दुई अङ्कको एउटा सङ्ख्या त्यसका अङ्कहरूको योगको चार गुणा छ । यदि अङ्कहरूको गुणनफल 18 भए त्यो सङ्ख्या र त्यसको विपरीत सङ्ख्या बिचको भिन्नता पत्ता लगाउनुहोस् । A number of two digits is equal to four times the sum of the digits. If the product of the digits is 18 then find the difference between the number and its reversing number.
Answer:
hence the number is 24.
Step-by-step explanation:
Two Solutions:
1.10x+y=4(x+y)
2x=y
2.10x+y+18=10y+x
x−y=−2
x−2x=−2
x=2
y=4
two digit number =24
1/3(6z + 7.2) = 0.5 (8z + 2) - 0.4
Answer:
z = 0.9
Step-by-step explanation:
1/3(6z + 7.2) = 0.5 (8z + 2) - 0.4
Step 1) (2z +2.4)=(4z+1) - 0.4
Step 2) (2z +2.4)=(4z+0.6)
Step 3) 1.8 = 2z
Step 4) 1.8/2 = z
Step 5) 0.9 = z
Answer:
.9
Step-by-step explanation:
it is 0.9 i did this assignment with my teacher
2. What political hurdles did African American representatives have to face after they went into
office?
The political hurdles that African American representatives have to face after they went into office is Racism.
What is Racism?Racism is the belief that different groups of humans have different behavioral traits that correspond to inherited characteristics and that they can be divided based on the superiority of one race over another.
Racism stems from the belief that a person is superior to others because of the color of their skin. In the olden days, blacks were excluded from public schools, denied the right to vote, and faced racism and legal discrimination almost everywhere. This is still faces in politics as well.
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The circumference of a circle is 7π ft. What is the area, in square feet? Express your answer in terms of
π
Answer:
49/4 π sq feet
Step-by-step explanation:
The circumference is the distance around a circle. The formula for circumference is:
C = πd
d stands for diameter. The circumference was given, 7π.
C = πd
= 7π
The diameter is 7. This is double the radius. The radius is half the circumference, so this radius is 7/2.
The area of the circle is:
Area = πr^2
= π(7/2)^2
= π(49/4)
=49/4 π
The area is 49/4 π
square feet.
Answer:
the answer is
12.25π ft
Which linear inequality is represented by the graph?
y ≤ One-halfx + 2
y ≥ One-halfx + 2
y ≤ One-thirdx + 2
y ≥ One-thirdx + 2
The linear inequality that is represented by the graph is; y ≤ One-halfx + 2
How to Interpret Inequality Graphs?
The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, from the inequality graph attached, we can see that we can calculate the slope from;
m = (y2 - y1)/(x2 - x1)
m = (3 - 2)/(2 - 0)
m = 1/2
We can also see that the y-intercept which is the point where the line crosses the y-axis is; y = 2.
The line is a solid line and not dotted and the shaded part is beneath the line and as such;
The inequality is; y ≤ One-halfx + 2
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What is k to the 5th power then triple the result
Answer: K^15
Step-by-step explanation:
The equation is (k^5)^3
To simplify this, we take the square root of 5-time square root 3 equal square root of 15
So the answer is k^15
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Manuel is riding his bike. The graph represents the distance Manuel travels from his house over time.
Describe what is happening as depicted in the graph.
Observing the nature of the graph and the pattern it develops relating time and distance covered by Manuel, The graph explains the nature of distance covered in bike with respect to time.
What is a graph?A representation of the relationship between two variables, often measured along one of two right-angled axes each.
What are different types of graphs?Different types of graphs are:
Statistical Graphs.Exponential Graphs.Logarithmic Graphs.Trigonometric Graphs.Frequency Distribution Graph.Manuel drives away from house for 2 units of time and stayed at a place for another 2 units of time. He start to bike towards the house for 2 units of time and again started to travel away for a single unit of time. He stayed at a place for 2 unit of time and bike back to the house in 5 units of time.
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Complete the sentences to compare the x- and y-intercepts for each function.
f(x) = -1/2 x + 10
g(x) = -4x - 12
The y-intercept of function fis
The x-intercept of function fis
but the y-intercept of function g is
but the x-intercept of function g is
The y-intercept of function f is 10 The x-intercept of function f is 20 but the y-intercept of function g is -12 but the x-intercept of function g is -3.
What are the x and y-intercepts?The places where a function or equation's graph crosses or "touches" the x-axis of the Cartesian Plane are known as the x-intercepts. This may be compared to a point with a y-value of zero. The locations where a function or equation's graph crosses or "touches" the y-axis of the Cartesian Plane are known as the y-intercepts. This may be compared to a point with a zero x-value.
Given two functions f(x) = -1/2 x + 10 and g(x) = -4x - 12
For function f(x)
Y-intercept of f(x) = -1/2 * 0 + 10 = 10
X-intercept of f(x) => -1/2x + 10 = 0
X-intercept of f(x) => x = 20
For function g(x)
Y-intercept of g(x) = -4*0 - 12 = -12
X-intercept of g(x) => -4x -12 = 0
X-intercept of g(x) => x = -3
Therefore, Function f's y-intercept is 10 Function f's x-intercept is 20, but the function g's y-intercept is -12 and its x-intercept is -3.
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if m/1 +m/5=234°, find m26=
Answer:
if m/1 +m/5=234°, find m26=
m26 = 234° - (1 + 5)m = 234° - 6m
m26 = 234° - 6(26)
m26 = 234° - 156°
m26 = 78°
Please help me! Find the value of X&Y for which ABCD must be a parallelogram!
Answer:
x = 8y = 6Step-by-step explanation:
You want the values of x and y that make the quadrilateral a parallelogram, given the halves of one diagonal are marked (3x-14) and (x+2), and the halves of the other diagonal are marked (4y-7) and (y+11).
ParallelogramThe diagonals of a parallelogram bisect each other. This means the marked segments on each diagonal are congruent.
x-value(3x -14) = (x +2)
2x = 16 . . . . . . . . . add 14-x
x = 8 . . . . . . . . divide by 2
y-value(4y -7) = (y +11)
3y = 18 . . . . . . . . . add 7-y
y = 6 . . . . . . . . divide by 3
The values of x and y are 8 and 6, respectively.
75 divided by 18 what do it equal
There is a sequence of numbers arranged in rows. Each row has six numbers. If the sequence begins as below, what is the fifth number on the 7853rd row?
0 1 2 3 4 5
6 7 8 9 10 11
12 13 14 15 16 17 ...
please help! I have a lot of points to give out lol
The fifth number in the 7853rd row as required to be determined is; 47,116.
What is the 7,853rd term of the arithmetic sequence?It follows from the task content that the fifth number on the 7853rd row of the sequence is to be determined. By observation, each column of the sequence of numbers represents an arithmetic sequence of numbers in which case;
The common difference is; 6 - 0 = 12 - 6 = 17 - 11 = 6.
Therefore, since the nth term of an arithmetic sequence is given by the formula;T (n) = a + (n - 1) d.
where a = does term
n = number of terms
d = common difference
In this scenario, the first term is the fifth number on the first row = 4.Therefore, the fifth number on the 7853rd row is; T (7853) = 4 + (7853 - 1) × 6T = 4 + (7852 × 6)T = 4 + 47,112T = 47, 116.
Therefore, the required number is; 47,116.
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To win the game, the team must score at least 8 goals. What inequality represents the number of goals, g, the team must score? Drag and drop the appropriate symbol to complete the inequality. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. g 8
The inequality represent the number of goals the team must score g ≥ 8.
What is inequality?An inequality show the relationship between two values in an algebraic equations that are probably not equal.
The statement about a game in which various teams are the playing:
It is given that To win that game, the team must scores at least 8 goals.
The meaning of word at least is that , the team can score either 8 goals or more than the 8 goals.
So, we will write this situation in terms of the inequality as follows:
The value of g will be greater than or equal to 8.
= g ≥ 8.
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xochitl has $2 worth of nickels and dimes. she has a total of 24 nickels and dimes altogether. graphically solve a system of equation in order to determine the number of nickels, x. and the number of dimes, y, that xochitl has
By using simultaneous linear equation, it can be calculated that
Xochitl has 8 nickels and 16 dimes
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Let the number of nickel Xochitl has be x and the number of dimes Xochitl has be y
She has a total of 24 nickels and dimes altogether
x + y = 24 .... (1)
Xochitl has $2 worth of nickels and dimes
0.05x + 0.1y = 2
5x + 10y = 200
x + 2y = 40 ..... (2)
From the graph, it is clear that the two simultaneous linear equation intersects at (8, 16)
So x = 8, y = 16
Xochitl has 8 nickels and 16 dimes
The graph has been attached
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The perimeter of AABC= 15 cm. Given that AB = 7 cm and /BAC = 60°, find the lengths of AC and BC and the area of the triangle.
Step-by-step explanation:
Call AB side a...which is 7
therefore b+c = 8 (editted this part due toarithmetic slip)
sketch it, use the cosine rule knowing cos 60 = 0.5and set up a simultaneous equation for the sides b+ c
7^2 = b^2+c^2 - bc
then
a + b = 15
(as this 2bcCOSA cancels down)
Todd is planning a vacation and is adding $5 per day towards his savings account for it. After 20 days he has a total of $150 in his savings
account.
a). Assuming this is linear relationship write an equation to model it.
b). How many days will it take Todd to build his savings up to a total of $250.
A) The equation of the model is 20x=100.
B) Todd will take 50 days to build his savings up to a total of $250.
What is meant by an equation?An assertion that two expressions containing variables or numerical values are equivalent is known as an equation. The first step in resolving a variable equation is to identify the values of the variables that lead to the equality being true. The variables that must be changed in order to solve the equation are referred to as the unknowns, and the unknown values that satisfy the equality are referred to as the equation's solutions.
1 day ------ $5
20 days -------?
x=20×5
x=$100
A) Let the savings per one day =$5
For 20 days it will be $100
And it is given as 20x=100
Where x=time in days
B) Todd has $150 dollars for 20 days
Actual savings for 20 days=100
? --------250
x=(20×250)/100
x=50 days.
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The tail of a 1-mile long train exits a tunnel exactly 3 minutes after the front of the train entered the tunnel. If the train is moving 60 miles per hour, how long is the tunnel? Hint : How far does the front of the train move in 3 minutes?
Answer:
The tail of a 1-mile long train exits a tunnel exactly 3 minutes after the front of the train entered the tunnel. If the train is moving 60 miles per hour, how long is the tunnel? Hint : How far does the front of the train move in 3 minutes?
Explanation
The front of the train moves 3 miles in 3 minutes. Therefore, the tunnel must be 1 mile long.
Answer:
2 miles long
Step-by-step :
The tail of the train starts one mile from the mouth of the tunnel and it must travel that distance plus the length of the tunnel in 3 minutes.
Let t = tunnel length
t + 1 = distance the tail must travel in 3 minutes.
3 minutes = 1/20 hr
(t+1) miles / 60 m/hr = 1/20 hr
t + 1 = 60/20
t+1 = 3
Subtract 1 from each side:
t = 2
The tunnel is 2 miles long.
If the derivative of y, dy/dx i the rate of change of y (alo known a the lope or gradient)
How can we ue the 2nd derivative of y, d2y/dx2 to determine whether the vertex of a quadratic i a maximum or minimum?
Why i thi the cae?
As d2y/dx2 is positive, the rate of change of gradient is positive, that means (2,-10) is a minimum point.
As stated in the video, the rate of change of dy/dx is the second derivative ( d2y/dx2 )
Thus, at a stationary point (dy/dx = 0), when d2y/dx2 < 0 meaning the rate of change of the gradient is negative the point is a maximum point. We can see that in the image below.
And at minimum points the rate of change of gradient is positive. Thus d2y/dx2 > 0 at minimum points.
A curve has equation y=x3 -12x +6 Find the coordinates of each stationary point, and the nature of these points (minimum or maximum).
Find when dy/dx = 0
dy/dx=3x2 -12
3x2 – 12 = 0
x2 =4
x = 2 or x=-2
when x = 2 y=-10 when x= -2 y=22
Thus, coordinates of stationary points are (2,-10) and (-2,22)
Now in order to find whether they are maximum or minimum points, we have to calculate d2y/dx2
d2y/dx2 = 6x
when x=2 d2y/dx2 = 12
As d2y/dx2 is positive, the rate of change of gradient is positive, that means (2,-10) is a minimum point.
when x= -2 d2y/dx2 = -12
As d2y/dx2 is negative, the rate of change of the gradient is negative, which means that (-2,22) is a maximum point
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Is this graph a function or nonfunction
Answer:
Not a function
Step-by-step explanation:
If we use the vertical line test, we can get an answer quite easily. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function.
If we were to move a vertical line across the above graph, it would touch two places, so therefore it is not a function.
HELPPPPPPPZZZZ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
x = 36
Step-by-step explanation:
First find the difference of size for the two givens sides on figure A and figure B. On figure A we have the given side 45, and Figure B the given size 27. Subtract the two to get 18. So the difference of scale is 18 for the two figures. So in order to find x just add the 18 to the 18 in figure B, and you get 36.
Please Help!!!! I will Brainlist!!! The question is in the picture!
Answer:
H=5
Step-by-step explanation:
25=1/2h(2+8)
25=1/2h(10)
25=10*h/2
what is dividend by 2 equals 25?
50
what times 10 equals 50?
5
Find the Surface area of the composite figure.
The surface area of the composite figure is 1856.53cm²(nearest hundredth)
What is a composite shape?A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes.
The figure has two shapes; a cylinder and an hemisphere.
Therefore the total surface area of the composite figure = surface area of cylinder + surface area of hemisphere.
The surface area of cylinder= 2πr(r+h)
= 2× 3.14 × 5.5( 5.5+40)= 1571.57cm²
The surface area of hemisphere= 3πr²
= 3×3.14×5.5²
= 284.96cm²
Therefore the surface area of the composite figure is 1571.57cm² + 284.96cm²= 1856.53cm²(nearest hundredth)
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Find the nth term of this quadratic sequence 4, 7, 12, 19, 28, ...
Answer:
which grafde are you in and I think ur question is wrong
a container is in a shape of a cuboid
the container is 2/3 full of water
a cup holds 275ml of water
what is the greatest number of cups that can be completely filled with water from the container
The greatest number of cups that can be completely filled with water is 2.
What is the greatest number of cups that can be completely filled with water from the container?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
The greatest number of cups that can be completely filled with water will be:
1000ml = 1 liter
2/3l = 667ml
Therefore, the number of cups will be:
= 667 / 275
= 2
The greatest number of cups is 2.
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