Answers
All three triangles are congruent as, △ABC ≅ △ACD ≅ △CBD under AA condition
What is the congruency of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.So, in the given image filling the blanks as follows:
(A) ∠ACB = ∠CDA = ∠CDB = 90° (Definition of right triangles)
(B) Triangle angle sum theorem:
∠CAD = ∠CBD = 90°∠CAD = ∠CBA = 90°∠CAD = ∠CAB = 90°It is enough to prove that:
△ABC ≅ △ACD ≅ △CBD under AA condition.(C) C.P.C.T (Corresponding parts of congurent triangles)
∠CBD = ∠CAD∠CAD = ∠CBD(D) △ABC ≅ △ACD ≅ △CBD under AA condition.
Therefore, all three triangles are congruent as, △ABC ≅ △ACD ≅ △CBD under AA condition
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Related Questions
4 3/20 as a simplified common fraction
Answers
Answer:[tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Please help with assignment (Due today)
Calculate the area of the shaded region in each figure. Use 3.14 for pi and round to the nearest hundredth, if necessary.
Answers
Answer:to question 1:55
Step-by-step explanation: area of purple 10 * 8=80 and then we subtract the area of the circle which is 25 so 80 minus 25=55
I did this like 3 weeks ago in 7 grade advance maths.
Minh borrowed $30,000 from a bank for a car loan. if the length of the car loan is 7 years and the intrest rate is 18%, what is the total amount he owes the bank at the end of the loan.
Answers
Including interest on the principal the total loan amount is $67800
A loan occurs when one or more individuals, businesses, or other entities lend money to additional individuals, businesses, or other entities.
A loan is obtained, and the recipient, or borrower, is typically liable for both the principal borrowed as well as interest payments until the debt is repaid.The principle amount borrowed, the interest rate the lender is charging, and the due date for repayment are often disclosed in the promissory note used to demonstrate the obligation. The subject asset(s) are temporarily divided between the borrower and the lender when a loan is issued.Interest on the loan = 30000 × 0.18 × 7 = $37800
Total amount to be paid = $ 30000 + $ 37800 = $67800
Hence he owes a total of $67800 to the bank.
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Solving Inequalities with One Variable
Show work
4+1+2≥5
Answers
Answer: The statement is true
4+1+2≥5
4+1+2 can be simplified to 7
7≥5, 7 is indeed greater than 5
how many hundreds multiplied by 4 will fit into 2018
Answers
We need to know numbers that multiplied by 4 are not greater than 2018.
For example, the number 100 (one hundred), when multiplied by 4 gives 400.
It obviously fits into 2018.
The number 900 by 4 gives 3600
Jan uses 7/8
yard of fabric for one quilt square and 1/7
yard in another. How much fabric has Jan used?
ASAP!!!
Answers
Jan used the total amount for fabric 57/56 yard.
The amount of fabric used by Jan can be calculated by performing addition of the individual values.
Total amount of fabric used = Amount used in one square + amount used in another square
Keep the values in formula to find the total amount of fabric used.
Total amount of fabric used = 7/8 + 1/7
Taking LCM, we get 56
Total amount of fabric used = (7×7 + 1×8)/56
Total amount of fabric used = (49 + 8)/56
Performing addition on Right Hand Side
Total amount of fabric used = 57/56
Thus, Jan used 57/56 yard of fabric.
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please help with this (percentages)
Answers
If it is asking you how much the tax would be, write down the first answer I give.
If it is asking you how much the item would be with tax included, wrote down the second answer I provide
11. $1.737 (or just $1.73 since there isn’t any currency that goes past the tenths place) or $30.687 ($30.68) total
12. $1.4256 (or $1.42) or $48.9456 ($48.94) total
13. $0.39 or $6.39 total
14. $2.60 or $67.60 total
15. $1.02 or $18.02 total
16. $3.60 or $51.6 total
Since the problem is now asking for the discounted price, you take new price then subtract it from the original price.
Problem 17, for example:
17. $56.25 - $11.25 = $45
18. $75
19. $12.792 (or $12.79 rounded)
20. $15.30
21. $93.75
22. $66.1
Hope this helps :-)
are the ratios 19:20 and 3:4 equivalent?
Answers
Answer:
no
Step-by-step explanation:
The ratios 19:20 and 3:4 are not equivalent. Both of them are in their simplest form.
pleaseeeee answer Separatrix Separation
Answers
The separatrix, which marks the transition from one type of motion to another, can typically be determined under straight forward circumstances.
We have to explain the separatrix separation.
When in motion, a pendulum can either swing from side to side or rotate continuously. The separatrix, which marks the transition from one type of motion to another, can typically be determined under straight forward circumstances. But when the pendulum is pushed at a nearly constant rate, the math breaks down.
A pendulum in motion has two possible motions: a continuous circle or a side-to-side swing. The separatrix—the point at which it switches from one kind of motion to another—can be estimated in the majority of straight forward circumstances. However, the mathematics breaks down when the pendulum is pushed at a nearly constant velocity.
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Please help me
Thank you ;)
Answers
Explanation:
SAS = side angle side
The tickmarks tell us which sides are congruent to one another. This forms one S of SAS.
The other S would be the shared overlapping sides between the triangles. We're using the reflexive property here.
The marked angles in red are congruent to one another, which refers to the 'A' in SAS. We have two pairs of congruent sides, and a pair of congruent angles between those sides. This allows us to use the SAS rule.
SSS can't be used since we don't know anything about the third pair of sides.
Two parrel lines cut by a transversal find each angle mesure
Answers
The angles formed between the parallel lines and the common transversal are;
7. [tex] \displaystyle{m \angle ABC = 92^{ \circ} }[/tex]
8. [tex] \displaystyle{m \angle MPQ = 125^{ \circ} }[/tex]
9. [tex] \displaystyle{m \angle MNP = 56^{\circ} }[/tex]
10. [tex] \displaystyle{m \angle WXZ = 130^{ \circ} }[/tex]
Corresponding angles
1 and 5, 2 and 6, 4 and 8, 3 and 7
Alternate interior angles
4 and 6, 3 and 5
Alternate exterior angles
1 and 7, 2 and 8
Same side exterior angles
1 and 8, 2 and 7
Same side interior angles
4 and 5, 6 and 3
What are parallel lines on a coordinate plane?Parallel lines on a coordinate plane are lines that have the same slope.
7. According to corresponding angle theorem, we have;
4•x° = (3•x + 23)°
Which gives;
4•x = (3•x + 23)
4•x - 3•x = 23
x = 23
[tex] \displaystyle{m \angle ABC = 4 \cdot x^{ \circ} = (4 \times 23)^{ \circ} = 92^{ \circ} }[/tex]
8. 5•x° = (3•x + 50)°
5•x - 3•x = 50
2•x = 50
x = 50 ÷ 2 = 25
[tex] \displaystyle{m \angle MPQ = (3 \cdot x + 50)^{ \circ} = (3 \times 25 + 50)^{ \circ} = 125^{ \circ} }[/tex]
9. According to alternate interior angles theorem we have;
2•a° = (a + 28)°
2•a° - a° = 28°
a = 28
[tex] \displaystyle{m \angle MNP = (a + 28)^{\circ} = (28 + 28)^{ \circ} = 56^{\circ} }[/tex]
10. 5•y = 2•y + 78°
5•y - 2•y = 78°
3•y = 78°
y = 78° ÷ 3 = 26°
y = 26°
[tex] \displaystyle{m \angle WXZ = 5•y = 5 \times 26^{\circ} = 130^{ \circ} }[/tex]
Corresponding angles
The corresponding angles are;
1 and 5, 2 and 6, 4 and 8, 3 and 7
Alternate interior angles
The alternate interior angles are;
4 and 6, 3 and 5
Alternate exterior angles
The alternate exterior angles are;
1 and 7, 2 and 8
Same side exterior angles
The same side exterior angles are;
1 and 8, 2 and 7
Same side interior angles
The same side interior angles are;
4 and 5, 6 and 3
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\frac{5}{8}-\frac{1}{8} 8 5 − 8 1
Answers
After solving the given fractions, the resultant fraction is 1/2.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when spoken in everyday English. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The terms with a numerator and a denominator are called fractions.So, 5/8 - 1/8:
Now, solve as follows:
5/8 - 1/8(5 - 1)/84/81/2
Therefore, after solving the given fractions, the resultant fraction is 1/2.
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The correct question is given below:
Solve: 5/8 - 1/8
Find the missing side of the triangle.A. 19−−√ miB. 22–√ miC. 11−−√ miD. 1 mi
Answers
From the right angled triangle given,
To find the missing side, x, of the triangle, Pythagorean theorem is applied
The Pythagorean theorem formula is
[tex]\begin{gathered} (\text{Hyp)}^2=(\text{Opp)}^2+(\text{Adj)}^2 \\ \text{Hyp is the hypotenuse} \\ \text{Opp is the opposite } \\ \text{Adj is the adjacent} \end{gathered}[/tex]The dimensions of the triangle are
[tex]\begin{gathered} \text{Hyp}=\sqrt[]{10}mi \\ \text{Opp}=xmi \\ \text{Adj}=3mi \end{gathered}[/tex]Substituting the values into the Pythagorean theorem formula above,
[tex]\begin{gathered} (\sqrt[]{10})^2=x^2+3^2 \\ 10=x^2+9^{} \\ \text{Collect like terms} \\ x^2=10-9 \\ x^2=1 \\ \text{Square root of both sides} \\ \sqrt[]{x^2}=\sqrt[]{1} \\ x=1 \end{gathered}[/tex]The missing side, x is 1mi
Answer is D
Here is a recipe for cupcakes.
• Terrance has cup of flour and eggs.
• Duri has cups of flour and grams of butter.
• Habib has cups of milk and cups of sugar.
• Anika has cup of sugar and cups of milk.
If each person has enough of all the other ingredients,
Answers
The number of cupcakes made by each person based on the limiting ingredients are;
Terrance → 6 cupcakes
Duri → 12 cupcakes
Habib → 12 cupcakes
Anika → 12 cupcakes
What is a limiting factor of a process or experiment?A limiting factor of a process is one that is used up completely upon completion of the process
The possible missing parts of the question are;
Recipe for making 12 cupcakes;
2 cups of flour
3/4 cups of sugar
2 eggs
3/4 cups of milk
125 g of butter
The ingredients each person has
Terrance; 1 cup of flour + 6 eggs
Duri; 12 cups of flour + 1,000 grams of butter
Habib; 3 cups of milk + 6 cups of sugar
Anika; 1 cup of sugar+ 4 cups of milk
Required;
The number of cupcakes each person can make on their own if each person has enough of the other ingredients.
Solution;
The question is with regards to the limiting variable or factor to making of the cakes
Terrance;
2 cups of flour bakes 12 cupcakes;
The number of cupcakes the 1 cup of flour Terrance has can bake is therefore;
(2 cups of flour)/2 = 1 cup of flour
(2 cups of flour)/2 bakes (12 cupcakes)/2 or 6 cupcakes
1 cup of flour bakes 6 cupcakes
Terrance can bake only 6 cupcakesDuri;
Duri has both more than the required number of cups of flour and grams of butter to make 12 cupcakes, therefore;
The number of cupcakes Duri can make given that he only has sufficient amounts of the other ingredients to make 12 cupcakes is therefore;
12 cupcakesHabib;
Habib also has more than the required amount of milk and sugar, but is limited by the other ingredients of which he only has enough to make 12 cupcakes, therefore;
The number of cupcakes Habib makes is 12Anika;
Anika also has more than the prerequisite amounts of sugar and milk to make 12 cupcakes, therefore;
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if A,B and C are three collinear points such that AB=10 units and AC=15, units what could be the length of BC?
Answers
The answer should be 25 unites
Conrad has 6 more marbles than Rory has. Let r represent the number of marbles that Rory has. Select the expression that represents the number of marbles that Conrad has.
Answers
Answer:
Conrad = r + 6
Step-by-step explanation:
So, it is R + 6
Solve and show your work
Answers
The most appropriate choice for factorization will be given by-
[tex](x - 6)(x - 3)[/tex] is the required factorization
What is factorization?
At first, it is necessary to know about algebraic expression.
Algebraic expressions consists of variables, numbers connected with operations like addition, subtraction, multiplication and division.
Factorization is the process of breaking an algebraic expression into a product of smaller expressions. Each smaller expression is known as factors of the algebraic expression
One of the technique of factorization is to do middle term breaking.
Factorization is a very important tool in mathematics
Here,
Middle term technique will be used.
[tex]2x^2 - 9x -18\\2x^2 - 12x + 3x -18\\2x(x-6)+3(x-6)\\(x-6)(2x + 3)[/tex]
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if i had 90 days and i did two months how many days do i have with the school breaks in it to ???
Answers
Answer:
Nothing cause your an special and you should know
Step-by-step explanation:
duh
x² + 16x + c = 0
What is the value of “c”
Answers
The equation can be solved as below
What is an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definitions of the word equation and its cognates in various languages might vary slightly. For instance, in French, an equation is defined as having one or more variables, but in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations.
The equation can be solved as
x² + 16x + c = 0
or, c = - x² - 16x
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Is this right? I really need to know
Answers
Yes, this is right. theta is angle C.
What are angles?In Euclidean geometry, an angle is made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles can be formed by two rays in the plane where they are placed. Additionally, when two planes overlap, angles are created. Dihedral angles are what they are called. When two straight lines or rays intersect at a single point, an angle is created. The vertex of an angle is the location where two points converge.
Here, angle is formed at C, A and B, but here B is 90 and the angle sign is given at C.
So, theta is angle C.
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9
Marisa needs to hire at least 10 staff members for an
upcoming project. The staff members will be made
up of junior directors, who will be paid $640 per
week, and senior directors, who will be paid $880 per
week. Her budget for paying the staff members is no
more than $9,700 per week. She must hire at least
3 junior directors and at least 1 senior director.
Which of the following systems of inequalities
represents the conditions described if x is the
number of junior directors and y is the number of
senior directors?
A) 640x+8800700
Answers
Answer:
$9,700=640x+880y+100 let me know if it is set up in a different way because I can only see a's answerStep-by-step explanation:
first we find out how much the required directors will take out of our budgetwe need 3 Jr and 1 SrJr get paid$640 a week and a Sr gets paid$880so we do 640×3=1,920now we add the Jrs and the Sr1,920+880=2,800so we are gonna subtract them from our total9,700-2,800=6,900we have $6,900 left we need at least 7 more employees so we need to figure out how much money we can spend for the next 7 employees6,900÷7= $985.7142857now we know how much we can spend at least $985 per employee we can hire 7 more Sr directors7×880= $6,160now we take that off the left over to see what we get6,900-6,160=740we can afford one more Jr director then we will have $100 remainingin total we can afford 8 Sr directors and 4 Jr directors with $100 remainingto put that in an equation it would be$9,700=640x+880y+1002. Amy was asked to find mABC in the picture. Her work is shown below.
The alternate interior angles are congruent when the lines
are paralled so
mLABC-3(27)-47
-81-47
-34°
30-47-n+7
-47
+47
3n-+54
-n-h
20-54
2
n=27
Explain Amy's mistake
A
(3n-47)
(n+7)
B
D
Show all work to find the correct mABC.
Answers
Amy's mistake was she took the angles as alternate interior angles, rather they form supplementary angles. The measure of both angles are 118 and 62.
What are alternate interior angles?The alternate interior angles theorem states that if a transversal connects two parallel lines, the alternate interior angles are identical in size. If we know the measure of the corresponding alternate interior angle, we may use this theorem to determine the measure of the alternate interior angle.
As per the given question,
both angles are not alternate interior angles,
rather both of the angles are supplementary angles.
This means that both form the sum of 180
⇒ 3n - 47 + n + 7 = 180
⇒ 4n - 40 = 180
⇒ 4n = 220
⇒ n = 55
∴ The measure of both angles will be 3n - 47 = 118 and n + 7 = 62
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Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(-7,-2); y= -3x + 1
Answers
the equation of line which passes through point (-7,-2) and is parallel to the graph of the given equation is y = -3x +23.
What is Algebraic expression ?
Algebraic expressions are numbers expressed using letters or alphabets without specifying their values. Algebra taught us how to express unknown values using letters such as x, y, and z. There can also be a single value that is placed before and multiplied by a variable in an algebraic expression in addition to these letters, which are called variables..
Here, the given equation is :
y = -3x + 1
which passes through point (-7,-2)
Let us first find the slope of line m which is parallel to the liney = -3x + 1 using point-intercept equation of line that is given by :
y = mx + c....(1)
y = -3x + 1
comparing above equation with equation (1) we get
m = -3
Now, the slope of line parallel to line y = -3x + 1 will have same slope that is m = -3
Now, Let us find the equation of the line using point-slope equation of line :
(y-y₁) = m(x-x₁)
Substituting all the values in above equation to get the equation of line :
(y-(-2)) = -3(x-(-7))
(y+2) = -3x-21
y = -3x -21 -2
y = -3x +23
Therefore, the equation of line which passes through point (-7,-2) is y = -3x +23.
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A virus is spreading around Kingwood. At the moment, 368 people are infected. If the virus is spreading at a rate of 6% each day, how many people in all will have caught the virus in 5 days?
Answers
Answer:
478 / 479
Step-by-step explanation:
6% of 368 is 22.08.
5 days = 6% x 5 = 30%.
30% of 368 = 110.4
110.4 + 368 = 478.4
492 people will be infected with the virus in 5 days.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
We have,
Number of people infected = 368
Rate of spreading = 6%
We can make an equation for the number of people infected in x days.
y = 368 x [tex](106/100)^x[/tex]
y = 368 x [tex]1.06^x[/tex]
Substitute x = 5
y = 368 x [tex]1.06^5[/tex]
y = 492.467
y = 492
Thus,
492 people will be infected with the virus in 5 days.
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Mr.peters has 80 sheets of colored paper.Seven of his students need the paper for a project.how many sheets does each student get? How many sheets are leftover?
Answers
Answer:
each student gets 1 sheet. There are 73 sheets left.
Step-by-step explanation:
Each student only needs 1 sheet and so you just do 80-7 and you get 73
There are 6 triangles and 2 squares. What is the simplest ratio of squares to total shapes?
Answers
Answer:
1:4
Step-by-step explanation:
6 triangles
2 squares
total number of shapes = 6 + 2 = 8
ratio of squares to total = 2/8 = 1/4
Answer: 1:4
I need help will give brainlist
Answers
Answer:
area of Δ K = 160 units²
Step-by-step explanation:
given scale factor of sides a , then
scale factor of areas = a²
here scale factor = 4 so factor of areas = 4² = 16
area of Δ J = [tex]\frac{1}{2}[/tex] × 5 × 4 = 10 units² , then
area of Δ K = 16 × 10 = 160 units²
if AB = 7x, CB = 5x + 8, and BD ⊥ AC, what is the length of CB?
Answers
Answer: 28
Step-by-step explanation:
Because BD ⊥ AC we can conclude that AB is equal to CB so we can set them equal to each other in an equation.
7x = 5x + 8
2x = 8
x = 4
Because X is 4 we can fill it into CB's expression.
5(4) + 8
20 + 8
28
The width of stamp M is 43 inches, and the length is 75 inches. The dimensions of stamp M are 76 times the dimensions of stamp P. What is the length of stamp P, in inches? A:6/5 B:8/7 C:14/9 D:49/3
Answers
If the dimensions of stamp M are 76 times the dimensions of stamp P then the length of stamp P in inches will be 75/76.
Given that the width of stamp M is 43 inches, length is 75 inches and the dimensions of stamp M are 76 times the dimensions of stamp P.
We are required to find the length of stamp P in inches.
Suppose the length of stamp P be x.
According to question, the length of stamp will be 76x.So,
75=76x
x=75/76
Hence if the dimensions of stamp M are 76 times the dimensions of stamp P then the length of stamp P in inches will be 75/76.
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Answer:
the answer is A, 6/5
what is the slope intercept form for x+3y=0
Answers
Answer:
y = -1/3 x
Step-by-step explanation:
what is the slope intercept form for x+3y=0
Slope intercept form solves for y:
x + 3y = 0
subtract x from both sides:
x + 3y - x = 0 - x
3y = -x
divide both sides by 3:
3y/3 = -x/3
y = -1/3 x
