determine if two triangles are necessarily congruent. if so in a flowchart proof to prove the they are.
Answers
Yes the two triangles are necessarily congruent as they are right angled so both the angles are equal and having two sides equal by using SAS rule that is Side, Angle, Side rule by the property of congruency.
What is Congruency?Two figures are considered to be "congruent" if they can be positioned precisely over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
What are the rules of congruency?If two triangles meet all 5 requirements for congruence, then they are congruent. They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SAS) (RHS).
Here the ΔCED and ΔPOR,
∠CED=∠POR
Side PR=CD
Side ED=PO
by using SAS rule,
ΔCED≅ΔPOR
Yes, the two triangles are inherently congruent because they have right angles, which means that both of their angles are equal, and because their sides are equal according to the SAS rule, which stands for Side, Angle, Side.
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Related Questions
13 FUNDRAISER The Cougar Pep Squad wants to sell T-shirts in the bookstore for
the spring dance. The cost in dollars to order T-shirts in their school colors is
represented by the equation C = 2t + 3.
a. Make a table of values that represents this relationship.
b. Rewrite the equation in function notation.
c. Graph the function.
d. Describe the relationship between the number of T-shirts and the cost.
Answers
Answer:
See attached worksheet.
Step-by-step explanation:
See attached worksheet for the table and graph.
I assume that "functation notation: simply means using x and y:
y = 2x + 3
The relationship between the number of T-shirts and cost is defined by y = 2t + 3, where:
y is the total cost,
x is the number of t-shirts,
the 2 is the cost for 1 t-shirt ($/t-shirt), and
3 is a one=time charge of $3 for each order.
The graph (attached) shows a straight line with a y-intercept of 3, the initial order fee. It is linear since the cost of a t-shirt remains the same egardless of order size.
evaluate 7*2*7*5 using properties of numbers. Name the property used in each step.
Answers
The simplified expression of 7 * 2 * 7 * 5 is 490
How to evaluate the expression?The expression is given as
7*2*7*5
Rewrite the expression properly
This is done as follows
7 * 2 * 7 * 5
The factors of the expression have different basis
i.e. Basis = 7 , 2 and 5
This means that we cannot apply the law of indices
Solving further, we have the following equation:
7 * 2 * 7 * 5 = 7 * 2 * 7 * 5
Rearrange the factors
So, we have
7 * 2 * 7 * 5 = 7 * 7 * 2 * 5
Evaluate the products of 7 and 7 in the above equation
So, we have
7 * 2 * 7 * 5 = 49 * 10
Finally, we have
7 * 2 * 7 * 5 = 490
Hence, the simplified expression of the expression given as 7 * 2 * 7 * 5 is 490
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The simplified expression of the given 7 x 2 x 7 x 5 will be; 490
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The expression is given as;
7 x 2 x 7 x 5
Rewrite the expression properly as follows;
7 x 2 x 7 x 5
The factors of the expression have different basis that is;
Basis = 7 , 2 and 5
Thus we can't apply the law of indices
Solving further, we have the equation;
7 x 5 x 7 x 2 = 7 x 2 x 7 x 5
Rearrange the factors;
7 x 2 x 7 x 5 = 7 x 7 x 2 x 5
7 x 2 x 7 x 5 = 49 x 10
Finally, we have the following
7 x 2 x 7 x 5 = 490
Hence, the simplified expression of the given 7 x 2 x 7 x 5 will be; 490
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-3a - 10 = 20
Solve the following equation
Answers
Answer:
a = -10
Step-by-step explanation:
-3a - 10 = 20
add 10 to both sides:
-3a - 10 + 10 = 20 + 10
-3a = 30
divide both sides by -3:
-3a/-3 = 30/-3
a = -10
Answer:
a=- 10
Step-by-step explanation:
-3a - 10 = 20
+10=+10
you end up with -3a=30
divide by -3 both side
a=-10
YAbisects ZXYZ. Which statement is false?A. YXYZB. ZXYA and ZZYA each measure 63º.C. ZXYA: ZZYAD. The total measure of ZXYA and ZZYA is 126º.
Answers
Given that
[tex]\vec{YA}\text{ bisesects}\angle XYZ[/tex]Then,
[tex]\begin{gathered} \angle XYA\text{ and }\angle ZYA\text{ each measure 63degr}ees \\ \angle XYA\cong\angle ZYA \\ \text{ The total measure of }\angle XYA\text{ and }\angle ZYA\text{ }is\text{ }63+63=126^{\text{0}} \end{gathered}[/tex]Therefore, the statement
[tex]\begin{gathered} \bar{YX}\cong\bar{YZ}\text{ is false} \\ The\text{ answer is Option A} \end{gathered}[/tex]Find the equation of a line that passes through (3,-1) and is perpendicular to the equation 3x+y=2
Answers
Answer:
y = (1/3)x - 2
Explanation:
First, we need to identify the slope of the equation 3x + y = 2, so we need to solve for x as:
[tex]\begin{gathered} 3x+y=2 \\ y=2-3x \end{gathered}[/tex]Now, the number beside the variable x is the slope, so the slope is -3
Then, two lines are perpendicular if the product of both slopes is equal to -1. It means that the slope m for our equation should be:
[tex]\begin{gathered} -3\cdot m=-1 \\ m=\frac{-1}{-3}=\frac{1}{3} \end{gathered}[/tex]Now, we can find the equation of the line using the following:
[tex]y=m(x-x_1)+y_1[/tex]Where m is the slope and (x1, y1) is a point on the line. So, replacing my 1/3 and (x1, y1) by (3, -1), we get:
[tex]\begin{gathered} y=\frac{1}{3}(x-3)+(-1) \\ y=\frac{1}{3}x-\frac{1}{3}\cdot3-1 \\ y=\frac{1}{3}x-1-1 \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]Therefore, the equation of the line is: y = (1/3)x - 2
Determine whether the two triangles are similar. If they
are similar, write the
similarity statement.
Answers
Answer:
not similar
Step-by-step explanation:
You want to know if two isosceles triangles are similar, given that one has a base angle of 78°, and the other has an a.pex angle of 16°.
Base angleThe base angles of the triangle with a.pex angle 16° will be ...
(180° -16°)/2 = 82° . . . . . . not 78°
SimilarityTwo isosceles triangles will be similar if they have congruent base angles. These triangles do not, so they are not similar.
by the time vince left the library he had 7/8 of his new book left to read ge read 1/10 of his book on the way home and 2/5 of the book after dinner what fraction of the book does he have left to read
Answers
We have the next information
When he left the library he read 8/8-7/8= 1/8
then he read 1/10
after dinner, he read 2/5
First, we need to sum the fraction of the book he read
[tex]\frac{1}{8}+\frac{1}{10}+\frac{2}{5}[/tex]we need to have the same denominator in order to sum the fractions
[tex]\frac{5+4+16}{40}=\frac{25}{40}=\frac{5}{8}[/tex]the book complete represent 8/8 so we need to subtract 5/8 from the fraction of the complete book
[tex]\frac{8}{8}-\frac{5}{8}=\frac{3}{8}[/tex]the fraction of the book does he have left to read is 3/8
A right triangle has a hypotenuse of length 3.80 m, and one of its angles is 31.0°. What are the lengths of the following sides?
Answers
Answer:
• (a)The length of the side opposite 31.0° is 1.96 meters.
,• (b)The length of the side adjacent 31.0° is 3.26 meters.
Explanation:
In the right triangle:
• The length of the hypotenuse = 3.80 m
,• Let the side ,opposite ,angle 31.0° = x
• Let the side ,adjacent ,angle 31.0° = y
(a)
From trigonometric ratios:
[tex]\begin{gathered} \sin\theta=\frac{Opposite}{Hypotenuse} \\ \implies\sin31.0\degree=\frac{x}{3.80} \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} x=3.80\times\sin31.0\degree \\ x=1.9571 \\ x\approx1.96\;m \end{gathered}[/tex]The length of the side opposite 31.0° is 1.96 meters.
(b)From trigonometric ratios:
[tex]\begin{gathered} \cos\theta=\frac{Adjacent}{Hypotenuse} \\ \implies\cos31.0\degree=\frac{y}{3.80} \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} y=3.80\times\cos31.0\degree \\ y=3.2572 \\ y\approx3.26\;m \end{gathered}[/tex]The length of the side adjacent 31.0° is 3.26 meters.
4. WATER Mr. Williams pays $40 a month
for city water, no matter how many
gallons of water he uses in a given
month. Let x represent the number of
gallons of water used per month. Let y
represent the monthly cost of the city
water in dollars. What is the equation of
the line that represents this information?
What is the slope of the line?
+0
Answers
The equation of the line that represents the information is y = $40.
The slope of the line is 0.
What is the equation and the slope?The equation that represents the total amount paid by Mr. Williams for the city water can be represented with a linear equation. A linear equation is an equation that is made up of a single variable that is raised to the power of one.
The form of a linear equation is:
y = ax + b
Where:
a = slope = which measures the rate of change of the equationb = intercepty = $40 + (x × 0)
y = $40
When shown on a graph, a linear equation can either slope upward, downward or have a slope of zero.
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find the missing value of x^2+14x+c
Answers
The value of missing number is [tex]49[/tex].
The given equation is [tex]x^{2}+14x+c[/tex].
We have to find the missing value of [tex]c[/tex].
We can find the value of [tex]c[/tex] by perfect square trinomial.
A perfect square trinomial is a equation which we can get after the square of binomial expression.
The equation [tex]ax^{2}+bx+c[/tex] said to be a perfect square if and only if it follows the condition [tex]b^{2}=4ac[/tex].
In the equation [tex]ax^{2}+bx+c[/tex], [tex]a,b[/tex] and [tex]c[/tex] are the real numbers.
Now we compare the given equation to [tex]ax^{2}+bx+c[/tex].
After comparing we get
[tex]a=1, b=14, c=c[/tex]
To find the value of [tex]c[/tex] we put the value of [tex]a,b,c[/tex] in expression [tex]b^{2}=4ac[/tex].
[tex](14)^{2}=4\times1\times c[/tex]
[tex]196=4\times c[/tex]
Divide by [tex]4[/tex] on both sides
[tex]\frac{196}{4}=\frac{4\times c}{4}[/tex]
[tex]c=\frac{196}{4} \\c=49[/tex]
Hence, the value of missing number is [tex]49[/tex].
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PLEASE HELP!! Thank you
Answers
Answer:16%
Step-by-step explanation: (New Number-Old Number)/Old Number*100
Meaning: [tex]\frac{290-250}{250} *100[/tex]
[tex].16*100[/tex]
16
Could be wrong but i j learned this
please help solve the attatched question pleasee
Answers
Using complementary angles, the numerical value of the given expression is as follows:
2.
What are complementary angles?Complementary angles are angles whose sum of the measures is of 90º.
The relevance of complementary angles in the context of this problem is that if a and b are complementary angles, then the sine of one angle is the cosine of the other angle, as follows:
sin(a) = cos(b).
Considering the angles of 40º and 50º in this problem, we have that:
sin(40º) = cos(50º).sin(50º) = cos(40º).Hence these following simplifications are applied:
sin²(40º) + sin²(50º) = sin²(40º) + cos²(40º) = 1.cos²(40º) + cos²(50º) = sin²(50º) + cos²(50º) = 1.sin(40º)cos(50º) = sin(40º)sin(40º) = sin²(40º).cos(40º)sin(50º) = cos(40º)cos(40º) = cos²(40º).Then the numerical value of the expression is given as follows:
1/1 + sin²(40º) + cos²(40º) = 1 + 1 = 2.
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Determine the number of terms in the arithmetic sequence below:-70, -69, -68, ..., 37, 38, 39, 40
Answers
Number of terms of sequence N
Difference D = -1
Then there are here
In negative part, 70 numbers
In positive x line, 40 numbers
And add also zero
Then, ANSWER IS
N= 70 + 40 + 1
. = 111
There are 111 numbers
What is the GCF of 64a^8b^4 and 56a^5b^8
Answers
We need to find the greatest common factor of
[tex]64a^8b^4,56a^5b^8[/tex]We will find the greatest common factor of 64 and 56, first
Since the factors of 64 are
[tex]\begin{gathered} 1\times64 \\ 2\times32 \\ 4\times16 \\ 8\times8 \\ 1,2,4,8,16,32,64 \end{gathered}[/tex]Since the factors of 56 are
[tex]\begin{gathered} 1\times56 \\ 2\times28 \\ 4\times14 \\ 8\times7 \\ 1,2,4,7,8,14,28,56 \end{gathered}[/tex]Then the common factors are 1, 2, 4, 8
The greatest is 8, then
The GCF of 64 and 56 is 8
The greatest common factor of the same variables is the least power
Then the GCF of a^8 and a^5 is a^5
The GCF of b^4 and b^8 is b^4
Then the greatest common factor of the given terms is
[tex]\text{GCF}=8a^5b^4[/tex]Please help 50 points!!!
Given: △ABC≅△BAD.
Prove: △AED≅△BEC.
Say what each proof was for each statement.
Answers
The proof of △AED is congruent to △BEC
What is congruency?
Two figures or objects are congruent in geometry if they have the same shape and size, or if one has the same shape and size as its mirror counterpart. In more technical terms, two sets of points are said to be congruent if and only if one of them can be changed into the other by an isometry, which is a combination of rigid movements such as translation, rotation, and reflection. This implies that one item may be relocated and reflected (but not scaled) to perfectly align with the other. So two separate plane figures on a piece of paper are congruent if they can be cut out and then entirely matched up. It is OK to flip the paper over.
Given, △ABC is congruent to △BAD.
and △AEB is common in both, so
△AED is congruent to △BEC (proved)
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what are the measures of <1 and <2 if they are in a 4:11 ratio
Answers
If the angles are complementary, we have that:
The measure of angle 1 is of 24°.
The measure of angle 2 is of 66°.
How to find the measures of ∠ 1 and ∠ 2 if they are in a 4:11 ratio?If two angles exists complementary, the sum of their measures exists 90°.
In this problem, we suppose that angles 1 and 2 exists complementary, therefore, m1 + m2 = 90
The measures of angle 1 and angle 2 are in a 4: 11 ratio, thus:
[tex]$m_1=\frac{4}{4+11}=\frac{4}{15}\left(m_1+m_2\right)$[/tex]
[tex]$m_2=\frac{11}{4+11}=\frac{11}{15}\left(m_1+m_2\right)$\\[/tex]
Considering m1 + m2 = 90
[tex]$m_1=\frac{4}{15}\left(m_1+m_2\right)=\frac{4}{15} \times 90=4 \times 6=24$[/tex]
[tex]$m_2=\frac{11}{15}\left(m_1+m_2\right)=\frac{11}{15} \times 90=11 \times 6=66$[/tex]
The measure of angle 1 is of 24º.
The measure of angle 2 is of 66º.
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What is the solution to 4x-5(2x-1) <= 7(2x+3)
Answers
Tom has 13 new magazines to read. Let M be the number of magazines he would have left to Read after reading R of them. Write an equation relating to M to R. Then graph your equation using the axis below
Answers
The equation that relates M to R is M = 13 - R
How to determine the equation that relates M to R?From the question, we have the following parameters:
Total number of new magazines = 13Number of magazines read = RNumber of magazines left = MThe total number of new magazines is the sum of the number of magazines read and the number of magazines left
This is represented as
Total number of new magazines = Number of magazines read + Number of magazines left
Substitute the known values in the above equation
13 = R +M
Make M the subject
M = 13 - R
Hence, the equation is M = 13 - R
See attachment for the graph
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What is the volume of the diagram below?
Answers
Answer: 11 units^2
Step-by-step explanation: count the blocks
What is 7h+(-9.1d)-13+6d-3.5h simplified
Answers
After simplification, 7h+(-9.1d)-13+6d-3.5h is 3.5h-3.1d-13.
According to the question,
We have the following expression:
7h+(-9.1d)-13+6d-3.5h
Now, we will simplify it by adding or subtracting the numbers or the numbers with the same variable together. For example, 3.5h can only be subtracted from 7h because both of them h as a variable. And 6d can be subtracted from 9.1d.
(More to know: when a positive and a negative number is multiplied then the result is always negative. In this case, we will multiply +1 into -9.1d.)
Now, let's simplify the given expression:
7h-3.5h-9.1d+6d-13
3.5h-3.1d-13
Hence, the expression obtained after solving the given expression is 3.5h-3.1d-13.
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What is the relationship between the two highlighted angles?
Answers
Angles 1 and 2 are remote interior angles while angle 3 exists as a remote exterior angle. The required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.
What is meant by triangle?The triangle exists a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.
A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.
Angles 1 and 2 are remote interior angles while angle 3 exists as a remote exterior angle. So there exists a property of a triangle in that the sum of the remote interior angles exists equivalent to the remote exterior angle.
∠1 +∠2 = ∠3.
Therefore, the required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.
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Complete the equation of the line through (-6,-5)(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and (-4,-4)(−4,−4)left parenthesis, minus, 4, comma, minus, 4, right parenthesis.
Answers
The equation of line that passes through the points (-6,-5) and (-4,-4) is x - 2y = 4 .
The equation of the line passing through the points (x₁,y₁) having slope as m is given by the formula .
y-y₁ = m(x-x₁)
In the question ,
it is given that
the required line passes through the points (-6,-5) and (-4,-4) ,
So , the slope(m) is = (-4 -(-5)/(-4 -(-6))
= (-4+5)/(-4+6)
= 1/2
the equation of the line passing through (-4,-4) and slope as 1/2 is
(y -(-4)) = (1/2)(x -(-4))
y + 4 = (x+4)/2
2y + 8 = x + 4
x - 2y = 8-4
x - 2y = 4
Therefore , The equation of line that passes through the points (-6,-5) and (-4,-4) is x - 2y = 4 .
The given question is incomplete , the complete question is
Complete the equation of line that passes through the points (-6,-5) and (-4,-4) .
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PLEASE HELP!!!!!
Which of the following equations represents the line that passes through the point (4, 3) and has a slope of 1/2?
A) 2x-3y=-18
B)2x-3y=17
C)3x-2y=-17
D)3x-2y-18
Answers
The equation of a line that passes through the point (4, 3) and has a slope of 1 / 2 is y = 1 / 2 x + 1.
How to find the equation of a line?The equation of a line that passes through a point can be describe as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line passes through (4, 3) and the slope is 1 / 2.
Hence, let's find the y-intercept using (4, 3)
y = 1 / 2 x + b
3 = 1 / 2 (4) + b
3 = 2 + b
b = 3 - 2
b = 1
Therefore, the equation of the line is y = 1 / 2 x + 1.
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Super Painters cobra S1.00 por pie cuadrado más una tarifa adicional de $ 25.00 para pintar una sala de estar. Ifx representa el área de las paredes de la sala de estar de Francesca, en pies cuadrados, e y representa el costo, en dólares, ¿qué gráfica representa mejor el costo de pintar su sala de estar
Answers
Responder
y = x + 25
Explicación
El costo de pintar y, para pintar x pies cuadrados es $ 25 más $ 1.00 por pie cuadrado.
Entonces, si se van a pintar x pies cuadrados, la tarifa será
y = (1 × x) + 25
y = x + 25
¡¡¡Espero que esto ayude!!!
Graph the linear equation. Help 50 points!!
Answers
First, let's edit the equation of the given line.
[tex]2y=2+3x[/tex][tex]y=\frac{2+3x}{2}[/tex]We were asked to identify three points. Let us give the value of [tex]x[/tex] as [tex]2,4[/tex] and [tex]6[/tex] respectively.
For [tex]x=2, y=4[/tex]For [tex]x=4, y=7[/tex]For [tex]x=6, y=10[/tex]Why did we give consecutive even numbers? Because our unknown is preceded by an odd number. We applied this to find the integer in the rational expression.
Finally, you will mark the three points we found on the coordinate plane. In the photo below, I have marked them for you.
nancy had 209 dollars to spend on 6 of the most mundane books.after buying them she had 17 dollars. on average, how much did each book cost
Answers
The average cost of each book that Nancy got is $32
What is cost?Cost refer to the amount or value of a product. cost is usually valued in money hence one has to pay some money to h]]get the commodity of choice
In the question, the commodity is mundane books
How to solve how much each book costgiven that
Nancy had 209 dollars to spend
number of books = 6
amount remaining after buying = $17
The question can be represented mathematically as
6x + 17 = 209
where x is the cost of the each book
6x + 17 = 209
6x = 209 - 17
6x = 192
dividing through by 6
6x / 6 = 192 / 6
x = 32
hence each book costs $32
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2. How do you determine the equation of the asymptote of an exponential function?
Answers
The general form of exponential function is given below:
[tex]\begin{gathered} y=a.b^x+c \\ \text{When a.b}^x=0,\text{ the asymptote of the function becomes } \\ y\text{ = c , which is, y-intercept} \\ \text{But where c=0, the asymptote is the line y = 0} \end{gathered}[/tex]find the equation of a line perpendicular to y=5x-3 that passes through the point (-5,3)?
Answers
The equation of the line that passes through point (-5,3) and perpendicular to y=5x-3 is y = -(1/5)x + 2.
What is the equation of line that passes through the given points and is perpendicular to the given line?The point-slope formula is expressed as
y - y₁ = m( x - x₁ )
Given the data in the question;
Equation of line: y = 5x - 3Point: (-5,3)First, determine the slope of the initial line using the slope intercept-form. y = mx + b
y = 5x - 3 compared with the slope intercept form,
Slope m = 5
Now, for the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.
Hence, slope of the perpendicular line is;
Slope m = -1/5
Next, find the equation of the perpendicular line, by using the point slope formula.
y - y₁ = m( x - x₁ )
Plug in the slope m ( -1/5 ) and point (-5,3).
y - y₁ = m( x - x₁ )
y - 3 = -1/5( x - (-5) )
y - 3 = -1/5( x + 5 )
y - 3 = -1/5(x) -5/5
y - 3 = -1/5(x) - 1
y = -1/5(x) - 1 + 3
y = -(1/5)x + 2
Therefore, the equation of the perpendicular line is y = -(1/5)x + 2.
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I need help with the question above. I took a pic.
Answers
Answer:
[tex]S=\frac{12}{5}[/tex]Step-by-step explanation:
The common ratio of the following sequence is:
[tex]\frac{\frac{9}{16}}{\frac{3}{2}}=\frac{3}{8}[/tex]If the common ratio is less than 1 or greater than -1 but not 0, we can use the following expression to determine the sum of the infinite geometric series:
[tex]S=\frac{a_1}{1-r}[/tex]Therefore, if we have a common ratio of 3/8 or 0.375 and the first term of the series is 3/2.
The sum would be:
[tex]\begin{gathered} S=\frac{\frac{3}{2}}{1-\frac{3}{8}} \\ S=\frac{\frac{3}{2}}{\frac{5}{8}} \\ S=\frac{24}{10}=\frac{12}{5} \end{gathered}[/tex]5. Eggs are packaged in cartons of 12.
Which of these numbers of eggs can be packaged
in full cartons? How do you know?
a) 96 b) 56 c) 60 d) 74
Answers
Answer: C) 60
Step-by-step explanation: If you keep adding 12 the only number that I get on the list is 60.
