The two-column proof that shows that ΔEAB ≅ ΔDCB by SAS congruence theorem is explained below.
What is the the SAS Congruence Theorem?The Side-angle-side congruence theorem (SAS) that states that two triangles that are have two pairs of corresponding congruent sides and a pair of included corresponding congruent angles are congruent to each other.
What is an Isosceles Triangle?Any triangle with two equal base angles is referred to as an isosceles triangle, The sides opposite these base angles are also congruent to each other.
Given the diagram below, the proof is expressed as follows:
Statement 1: ΔEAB and ΔDCB are two right triangles
Reason 1: Given
Statement 2: ∠EAB ≅ DCB
Reason 2: Right angles
Statement 3: ∠BED ≅ BDE
Reason 3: Given
Statement 4: ΔBED is an isosceles triangle
Reason 4: Definition of isosceles triangle
Statement 5: BE ≅ BD
Reason 5: Definition of isosceles triangle
Statement 6: ΔEAB ≅ ΔDCB
Reason 6: SAS
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Si un buzo se sumerge 4 metros luego sube 2 metros y finalmente desciende 5 metros más, ¿a qué profundidad se encuentra al final de su recorrido ?
Así, concluimos que la posición final del buzo será 7 metros bajo la superficie del agua.
¿a qué profundidad se encuentra al final de su recorrido?Primero, vamos a definir la superficie del agua como el 0 metros.
Sí sabemos que primero el buzo se sumerge 4 metros, entonces en este punto la posición del buzo es:
P = 0m - 4m = -4m
Luego el buzo sube 2 metros, entonces la nueva posición será:
P = -4m + 2m = -2m
Finalmente, el buzo desciende otros 5 metros, entonces la posición final del buzo será:
P = -2m - 5m = -7m
Así, concluimos que la posición final del buzo será 7 metros bajo la superficie del agua.
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The perimeter of a football field is 1040 feet. The length of the field is 120 feet less than 3 times the width. What are the dimensions of the field?
Answer:
length: 360 ftwidth: 160 ftStep-by-step explanation:
The perimeter formula and the given relation between length and width can be used to write and solve an equation for the field dimensions.
SetupLet w represent the width of the field. Then (3w-120) is the length of the field, and its perimeter is ...
P = 2(L +W)
1040 = 2((3w-120) +w)
SolutionDividing by 2 and simplifying, we have ...
520 = 4w -120
130 = w -30 . . . . . . divide by 4
160 = w . . . . . . . . . add 30
3w-120 = 3(160) -120 = 360 . . . the field's length
The dimensions of the field are 160 feet long by 360 feet wide.
A circle has a circumference of 50.24 units.
What is the radius of the circle?
Use 3.14 for π and enter your answer as a decimal.
units
Answer: 8 units
Step-by-step explanation:
Danni thinks of a number. She subtracts 2 then multiples the result by 8. The answer is the same as subtracting 5 from the number then multiplying by 16. What is the number did Danni think of?
Answer:
8
Step-by-step explanation:
let the number=x
8(x-2)=16(x-5)
divide by 8
x-2=2(x-5)
x-2=2x-10
2x-x=-2+10
x=8
how do i write 4x+5y=20 in slope intercept form
Answer:
Y=mx+b
Step-by-step explanation:
The answer is y = -4/5x + 4.
We know the general form for slope intercept form is :
y = mx + c
The given equation is in standard form.
4x + 5y = 20
Bring 4x to the other side by subtracting 4x on both sides.
4x + 5y - 4x = 20 - 4x
5y = -4x + 20
Divide 5 on both sides to isolate the variable y.
5y x 1/5 = 1/5 x (-4x + 20)
y = -4/5x + 4
A company makes Japanese-style lunch boxes called bento boxes. Each bento box is a cube with-foot-long edges. The company ships the bento boxes in a container in the shape of a rectangular prism that measures feet by feet by feet. A manager correctly finds the volume of the container using a formula. An employee double-checks the calculation by packing the container full of bento boxes. Use the drop-down menus to explain how both volume calculations compare. Click the arrows to choose an answer from each menu. The manager can find the volume of the container using the formula Choose... The employee correctly determines that the container can be filled with Choose... bento boxes. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the Choose... of one bento box. The volume found by using the formula is of bento boxes in the container. Y Choose... ▼ the volume of the total number
The volume of a container shows the amount of space that it has inside of it.
The use of bento boxes that has edges that are a foot long and the use of a rectangular-shaped container to ship it would have been more useful if the dimensions were provided.
How to calculate volume?Provided that the dimensions are provided, the formula that can be used to find the volume of a container is:
V = L × W × H
Where:
L= Length
W= Width
H= Height
It is worthy to note that your question is incomplete as you did not include the answer choices for how the manager found the volume of the container and other questions so a general overview was given.
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The manager can find the volume of the container using the formula lwh. The employee correctly determines that the container can be filled with 3 layers of 21 bento boxes. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the volume of one bento box. The volume found by using the formula is equal to the volume of the total numberof bento boxes in the container.
A rectangular dining room has an area of 64 m². Its perimeter is 32 m. What are the dimensions of the dining room
Given the area and perimeter of the rectangular dining room, the dimensions of the dining room are 8m by 8m.
What are the dimensions of the dining room?The area of rectangle is expressed as;
A = l × b
The perimeter of a rectangle is expressed as;
P = 2( l + b )
Given that;
Area of the rectangular dining room A = 64m²Perimeter of the rectangular dining room P = 32mLength of the rectangular dining room l = ?Breadth of the rectangular dining room b = ?We use the information given to form a system of equations.
A = l × b
64 = l × b
P = 2( l + b )
32 = 2( l + b )
Hence, we have;
64 = l × b --------- equ 1
32 = 2( l + b )-----equ 2
Lets make l the subject of the formula in equation 1
64 = l × b
l = 64/b -------------equ 3
Substitute equation 3 into equation 2
32 = 2( l + b )
32 = 2l + 2b
32 = 2(64/b) + 2b
32 = 128/b + 2b
Now, we solve for b.
32 = 128/b + 2b
32 - 2b = 128/b
32b - 2b² = 128
2b² - 32b + 128 = 0
We factor out 2
2( b² - 16b + 64) = 0
From perfect square rule
2( 8-b )² = 0
divide both side by 2 and take the square root of both side
( 8-b )² = 0
8-b = 0
b = 8
Substitute b=8 into equation 1
64 = l × b
64 = l × 8
l = 64/8
l = 8
Given the area and perimeter of the rectangular dining room, the dimensions of the dining room are 8m by 8m.
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In a certain school 70% of the students in first-year chemistry have had algebra. If there are 290 students in first-year chemistry, how many of them have had algebra?
2.
David swam 800 m in 20 minutes. Find his average speed in m/min.
Answer:
40 meters a minute
Step-by-step explanation:
800m - 20 min
800/20
40m-1 min
which equation shows that the Pythagorean identity is true for 0 = 180 degrees? select the equation that is in the form sin^2 0+cos^2 0=1
A. 0^2 + (-1)^2 = 1
B. 1^2 + 0^2 = 1
C. 0^2 + 1^2 = 1
D. (-1)^2 + 0^2 = 1
The equation in the form of the given expression is (0)² + (1)² = 1
Trigonometry identityAccording to some of the trigonometry identity
sin 0 = 0
cos 0 1
Given the expression below
sin^2 0+cos^2 0=1
This can also be expressed as:
(sin0)² + (cos0)² = 1
Substitute
(0)² + (1)² = 1
Hence the equation in the form of the given expression is (0)² + (1)² = 1
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The radius of a circle is 9.5 cm find the circumference to the nearest tenth
For circumference use C = 2πr because π is the ratio of Circumference to diameter and diameter is 2 x radius.
C = 2 x 3.142 x 9.5 cm ≈ 59.7 cm
Area of a circle is π x r² = 3.142 x (9.5 cm)² ≈ 283.6 cm²
The circumference of a circle with a radius of 9.5 centimeters is about 59.7 centimeters and the area of a circle with radius of 9,5 centimeters is about 283.6 centimeters.
Calculate the perimeter and area of this shape.
Perimeter =
Perimeter → 25cm
Area → 25.5cm²
Explanation:[tex]perimeter = > 2.5 \times 2 + 5.5 + 3.5 + 6 + 3 + 2 = 5 + 9 + 9 + 2 = 25[/tex]
[tex]area = > 3 \times \frac{1}{2} \times 2 + 3 \times 3.5 + 6 \times 2 = 3 + 12 + 10.5 = 25.5[/tex]
The line 2x + 3y - k = 0 bisects the line segment joining the points A(4, -3) and B(-2, 5). Find the value of k.
Answer:
5
Step-by-step explanation:
The midpoint of segment AB is (1, 1).
Substituting these coordinates into the equation of the line,
[tex]2(1)+3(1)-k=0 \\ \\ 5-k=0 \\ \\ k=5[/tex]
I need help solving
The graph of the translated function can be seen in the image below.
How to translate the graph of a function?
For a given function f(x), we define a vertical translation of N units as:
g(x) = f(x) + N
Where if N is positive, the translation is upwards. If N is negative, the translation is downwards.
In this case, we have:
y = f(x) - 2
Then we just need to translate the given graph 2 units below, we will get the graph you can see below.
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Roberto has 5 more than twice the number of tee shirts that Brisa has. Roberto has 19 tee shirts. How many tee shirts does Brisa have?
Answer:
Step-by-step explanation:
Determine the number of lines of symmetry and the number of rotation symmetries for each of the following sea organisms.
There are 9 lines of symmetry and infinite rotational symmetries in first figure,4 lines of symmetry and no rotational symmetries in second figure,6 lines of symmetry and infinite rotational symmetries in third figure,1 line of symmetry and infinite rotational symmetries in fourth figure.
Given four figures.
We are required to find the number of lines of symmetry and rotational symmtries.
Symmetry lines are those lines which act as shape in such a way that both parts are like mirror image.
Rotational symmetry is the property that a shape has when it looks same after some turn.
There are 9 lines of symmetry and infinite rotational symmetries in first figure.There are 4 lines of symmetry and no rotational symmetries in second figure.There are 6 lines of symmetry and infinite rotational symmetries in third figure.There is 1 line of symmetry and infinite rotational symmetries in fourth figure.Hence there are 9 lines of symmetry and infinite rotational symmetries in first figure,4 lines of symmetry and no rotational symmetries in second figure,6 lines of symmetry and infinite rotational symmetries in third figure,1 line of symmetry and infinite rotational symmetries in fourth figure.
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In the rectangular prism below, the length of MR is 9 feet, the length of RS is 12 feet, and the length of ST is 5 feet. What is the length of the line
segment drawn from point T to point M?
Answer:
a
Step-by-step explanation:
[tex]\sqrt{9^2 + 12^2 + 5^2}=\sqrt{250}=5\sqrt{10}[/tex]
State and prove De Moivre's theorem
Answer:
assume the formula is true for n is equal to k prove that result is true for n is equal to k + 1 hence result proves since the thorum is true for n is equal to 1 and n k + 1 is unit through a and
Find the simple interest.
$2000 at 6% for 6 months
The simple interest is $____
(Round to the nearest cent as needed.)
Answer:
I think it's 120 dollars sorry if i get it wrong but I am sure it is right tell me when you get the right answer byeeee.
Asap help with this PLEASE
Answer:
124.5°
Step-by-step explanation:
Let the smallest angle be x. Then, the sum of the angles is an arithmetic sequence with first term x, common difference 7, and 8 terms.
Using the sum of an arithmetic series formula,
[tex]\frac{8}{2}(2x+(8-1)(7))=1080 \\ \\ 4(2x+49)=1080 \\ \\ 2x+49=270 \\ \\ 2x=221 \\ \\ x=110.5[/tex]
So, the third angle is 110.5+14=124.5
Need help with this question
Answer:
y=-1/2n+44
Step-by-step explanation:
The number of bean stalks, n, represents the x values
The yield, y, represents the y values
After reading the problem, we have two coordinates: (30,29) and (32, 28) Because this problem is asking for y=mn+b, we have to find the slope. How do we find the slope? We do so by using the slope formula y2-y1/x2-x1. Now let's input the coordinates into this formula.
1.) 28-29/32-30 = -1/2
Let's plug -1/2 into y=mn +b
2.) y=-1/2n+b
Now we have to find what b ( y intercept) equals. To find B, we plug a coordinate into x and y. Let's use (30,29)
3.) 29 = -1/2(30)+b
29 = -15 +b
44 = b
We have now found the linear relationship form for this problem: y=-1/2n +44
A Community theater sold 63 tickets to the afternon fora total of 444 birr, an adult ticket Cost 8 birr achild ticket cost 4 bir, and a senior ticket cost 6 birr. If twice as many tickets were sold to adults as to Children and seniors combined how many of each tick were sold ? ( Use Gaussian elimination method)
The number of tickets sold are:
30 children tickets were sold33 adult tickets were soldHow to determine the number of tickets sold to children and seniors?From the question, we have the following parameters:
Number of tickets = 63
Total amount = 444 Birr
Adult ticket = 8 Birr per adult
Children ticket = 6 Birr per adult
Represent the children tickets with x and adults ticket with y.
So, we have the following system of equations
x + y = 63
6x + 8y = 444
Express the equations as a matrix
x y
1 1 63
6 8 444
Apply the following transformation
R2 = R2 - 6R1
This gives
x y
1 1 63
0 2 66
Apply the following transformation
R2 = 1/2R2
x y
1 1 63
0 1 33
From the above matrix, we have the following system of equations
x + y = 63
y = 33
Substitute y = 33 in x + y = 63
x + 33 = 63
Subtract 33 from both sides of the above equation
x = 30
Hence, 30 children tickets were sold and 33 adult tickets were sold
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please help urgently
Solving for y:
6y - 2x = 20
6y = 2x + 20
y = [tex]\frac{2x + 20}{6}[/tex]
y = [tex]\frac{2x}{6} + \frac{20}{6}[/tex]
y = [tex]\frac{1x}{3} + \frac{10}{3}[/tex]
Hope it helps!
Answer:
Step-by-step explanation:
6y - 2x = 20
-6 -6
-2x = 20 - 6y
divide both sides by -2
[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{20 - 6y}{-2}[/tex]
Dividing by -2 undoes the multiplication by -2.
[tex]x = \frac{20 - 6y}{ -2}[/tex]
Divide 20 -6 by -2
x = 3y - 10
Or
y = [tex]\frac{10}{3}[/tex]x +[tex]\frac{x}{3}[/tex]
The equation 2x = 3y − 5 when written in slope-intercept form
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
What does the problem want us to find:
[tex]\hookrightarrow \text {Slope-intercept form}[/tex]
What is the slope-intercept form:
[tex]\hookrightarrow \text {it is when the function has the y-variable isolated by itself to one side}\\\hookrightarrow \text{and everything else to the other side}[/tex]
Let's apply our knowledge:
[tex]2x =3y-5\\-3y=-5-2x\\y=\frac{2}{3} x+\frac{5}{3}[/tex]
Answer:[tex]y=\frac{2}{3} x+\frac{5}{3}[/tex]
Hope that helps!
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urgent help thank you
Answer:
-4
Step-by-step explanation:
7x^3 + 5x^2 - 2
= 7*-1 + 5*1 - 2
= -7 + 5 - 2
= -4
A total of 646 tickets were sold. They were either adult ticket or student tickets. There were 54 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
350
Step-by-step explanation:
Let the number of adult tickets be x, then the number of student tickets sold would be (x–54).
We now have
x+(x–54)=646
2x=700
x=350
Therefore, 350 adult tickets were sold.
Alicia wanted to lose some weight, so she planned a day of exercising. She spent a total of 3 hours riding her bike and jogging. She biked for 12 miles and jogged for 12 miles. Her rate for jogging was 6 mph less than her biking rate. What was her rate when jogging?
Please answer asap thank you :)
Using the relation between velocity, distance and time, it is found that her jogging rate was of 6 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
Jogging, her velocity was of v, while the time was of t, for a distance of 12 miles, hence:
[tex]v = \frac{12}{t}[/tex]
Biking, her velocity was of v + 6, while the time was of 3 - t, for a distance of 12 miles, hence:
[tex]v + 6 = \frac{12}{3 - t}[/tex]
[tex]v = \frac{12}{3 - t} - 6[/tex]
Then:
[tex]\frac{12}{t} = \frac{12}{3 - t} - 6[/tex]
[tex]\frac{12}{3 - t} - \frac{12}{t} = 6[/tex]
[tex]\frac{12t - 36 + 12t}{t(3 - t)} = 6[/tex]
18t - 6t² = 24t - 36
6t² + 6t - 36 = 0
t² + t - 6 = 0
(t + 3)(t - 2) = 0. -> t = 2 hours.
Hence her jogging rate in mph is given as follows:
[tex]v = \frac{12}{2} = 6[/tex]
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(questions in image)
A. Which plane contains line b?
B. Name 3 Collinear Points
C. Name the plane containing point W
D. Name two points not coplanar with points T and Q
E. At which line do the planes M and N intersect
Answer:
1. Plane N
2. Points P, Q, R
3. Plane CRW …
4. Points K and H
5. Line a
Which statement correctly compares functions f and g? function f function g An exponential function passes through (minus 1, 5), and (2, minus 1.5) intercepts axis at (1, 0), and (0, 2) Function g is a decreasing exponential function with a y-intercept of 5 and no x-intercept. A. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. B. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. C. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞. D. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞.
A statement correctly compares functions f and g is that: C. they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
What is a function?A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).
The types of function.In Mathematics, there are different types of functions and these include the following;
Periodic functionInverse functionModulus functionSignum functionPiece-wise defined function.Function g is represented by the following table and a line representing these data is plotted in the graph that is shown in the image attached below.
x -1 0 1 2 3 4
g(x) 24 6 0 -2
Based on the line, we can logically deduce the following points:
y-intercept approaches -2.43 to 24.86.x-intercept approaches negative infinity (-∞) to infinity (∞).This ultimately implies that, a statement correctly compares functions f and g is that both functions have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
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What is the radius and diameter of the following circle?
Radius = cm
diameter= cm
The value of diameter and radius of circle is 7 cm and 3.5cm.
According to the statement
we have given that the a figure of circle and we have to find the radius and the diameter of the circle.
So, We know that the
The radius of a circle runs from its center to its edge, the diameter runs from edge to edge and cuts through the center.
Here from the figure it is clear that the
Diameter of circle = 7cm
and the radius of circle we have to find
So,
Radius of circle = Diameter /2
Substitute the values in it then
Radius of circle = 7cm /2
Radius of circle = 3.5 cm.
So, The value of diameter and radius of circle is 7 cm and 3.5cm.
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