Answers
Given:
• Length of side adjacent the indicated angle = 48
,• Length of hypotenuse = 56
Let's find the measure of the indicated angle.
To find the measure of the indicated angle, apply the trigonometric ratio formula for cosine:
[tex]cos\theta=\frac{adjacent}{\text{ hypotenuse}}[/tex]Thus, we have:
[tex]\begin{gathered} cos\theta=\frac{48}{56} \\ \\ cos\theta=\frac{6}{7} \\ \\ \text{ Take the inverse cosine of both sides:} \\ \theta=cos^{-1}(\frac{6}{7}) \\ \\ \theta=31^o \end{gathered}[/tex]Therefore, the measure of the indicated angle is 31 degrees.
ANSWER
Related Questions
The table shows information recorded about the location and speed of an airplane during an overseas flight.
a) Determine the altitude in miles.
b) Determine the ground speed in miles per hour.
c) Determine the headwind in miles per hour.
d) Determine the temperature in degrees Fahrenheit using the formula
F=9/5 C+32
Answers
Part a
The altitude in miles = 6.07 miles
Part b
Head wind in miles per hour = 439.30 miles per hour
Part c
The headwind in miles per hour = 114.35 miles per hour
Part d
The temperature in degree Fahrenheit = -41.8 degrees Fahrenheit
Part a
The altitude = 9770 meters
To convert meter to miles, divide the length by 1609
Therefore,
9770 meters = 9770/1609
=6.07 miles
Part b
The ground speed = 707 km/hours
To convert km per hour to miles per hour, divide the speed value by 1.609
707 km/hour = 707/1.609
= 439.30 miles per hour
Part c
The head wind = 184 km/hour
To convert km per hour to miles per hour, divide the speed value by 1.609
184 km/hour = 184/1.609
= 114.35 miles per hour
Part d
The outside air temperature = -41 degree C
F = (9/5)C + 32
= (9/5)×-41+32
= -41.8 degrees Fahrenheit
Hence,
Part a
The altitude in miles = 6.07 miles
Part b
Head wind in miles per hour = 439.30 miles per hour
Part c
The headwind in miles per hour = 114.35 miles per hour
Part d
The temperature in degree Fahrenheit = -41.8 degrees Fahrenheit
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The mean of 40,50 and 90 is P. If the mean of 40,50,90 and P is Q. What is the value of Q
Answers
Given:-
The mean of 40,50 and 90 is P. If the mean of 40,50,90 and P is Q.
To find:-
The value of Q.
So now the mean of 40,50 and 90 is P. so we get,
[tex]\frac{40+50+90}{3}=\frac{180}{3}=60[/tex]So the value of p is 60.
Also we have the mean of 40,50,90 and P is Q. so we get,
[tex]\frac{40+50+90+60}{4}=\frac{240}{4}=60[/tex]So the value of q is 60.
Ubicar las siguientes fracciones en la recta numérica: 3/9
Answers
The most appropriate choice for Number line will be given by -
The number line has been shown in the figure attached.
What is a number line?
A visual representation of the real numbers can be shown on a diagrammatic representation of graduated straight lines. The visual representation of the real numbers is known as the number line. Number line can be used for addition or subtraction of two numbers.
Here,
The number line has been attached
[tex]\frac{3}{9}[/tex] lies between 0 and 1
So the space between 0 and 1 is divided into 9 equal parts as the denominator of the given fraction is 9
Now the third small line is the required value i.e [tex]\frac{3}{9}[/tex] as 3 is in the numerator of the given fraction
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True or false?
In centrally planned economies, the distribution of goods costs nothing to administer
Answers
The following statement "In centrally planned economies, the distribution of goods costs nothing to administer" is true.
A centrally planned economy, often known as a command economy, is an economic system in which a government agency makes economic choices affecting the production and distribution of products. Centrally planned economies vary from market economies in that these decisions are the outcome of hundreds of choices made by producers and consumers.
State-owned corporations provide goods and services in planned economies, however, independent firms may occasionally be brought into economic planning. Prices, salaries, and production schedules are often set by a centralized bureaucracy.
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Which value of X Satisfy 2(x +5.3) =4.2
Answers
SOLUTION
This question simply means we should find the value of x,
[tex]2\mleft(x+5.3\mright)=4.2[/tex]First we expand by using 2 to multiply the items in the bracket, we have
[tex]\begin{gathered} 2\times x+2\times5.3=4.2 \\ 2x+10.6=4.2 \\ 2x=4.2-10.6 \\ 2x=-6.4 \\ \text{dividing both sides by 2, we have } \\ \frac{2x}{2}=\frac{-6.4}{2} \\ x=-3.2 \end{gathered}[/tex]Hence the answer is -3.2
I just need to quickly know if my answers are correct thank you!
Answers
1) All of these questions are about evaluating those functions for each input.
9) So, let's check them out evaluating each one.
[tex]\begin{gathered} f(4)\Rightarrow f(x)=(\frac{1}{2}x)+13 \\ f(4)=(\frac{1}{2}\cdot4)+13 \\ f(4)=2+13\Rightarrow f(4)=15 \\ D \end{gathered}[/tex]10)
[tex]\begin{gathered} f(x)=\frac{3}{5}x-10 \\ f(5)=\frac{3}{5}(5)-10 \\ f(5)=3-10 \\ f(5)=-7 \end{gathered}[/tex]11)
[tex]\begin{gathered} f(x)=x^2+7 \\ f(-1)=(-1)^2+7\Rightarrow f(-1)=1+7\Rightarrow f(-1)=8 \end{gathered}[/tex]12)
[tex]\begin{gathered} f(x)=3x^3-12x^2 \\ f(2)=3(2)^3-12(2)^2 \\ f(2)=24-48 \\ f(2)=-24 \end{gathered}[/tex]Discuss the relationship between the discriminant of a quadratic polynomial and the quantity of real roots it possesses. Explain the positioning of the roots of the polynomial on its graph with respect to the discriminant and the sign of the discriminant.
Answers
The relationship between the discriminant of a quadratic polynomial and the number of real roots is that the discriminant let us know the number and type of the solutions.
Basically for a quadratic polynomial ax²+ bx + c = 0, the b² - 4ac is the discriminant.if the discriminant is greater than zero (b²- 4ac > 0), the graph intersects the abscissa twice which means it has two real solutions, whereas if the discriminant is equal to zero ( b² - 4ac = 0), then the graph intersects once the abscissa which means it has a single real solution and at last if less than zero (b² - 4ac < 0), then the graph doesn't at all intersect the abscissa which, it has imaginary solutions.
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Simplify the expression. Write your answer as a power.(-8.3)8 (-8.3)4(-8.3)? (-8.3)3The simplified expression is
Answers
This will be simplified with this law of indices
[tex]\frac{a^e}{a^y}=a^{e-y}[/tex][tex]\begin{gathered} \text{Therefore the initial question becomes:} \\ ((-8.3)^{8-7})\text{ }\cdot\text{ (}(-8.3)^{4-3}) \end{gathered}[/tex][tex]\begin{gathered} (-8.3)^1\cdot(-8.3)^1 \\ (-8.3)^{1+1} \\ (-8.3)^2 \\ \end{gathered}[/tex]Going further, we can simplify to:
[tex]\begin{gathered} (-8.3)\times(-8.3) \\ =68.89 \end{gathered}[/tex]At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the standard error for the sample mean?
0.029
0.050
0.120
0.091
Answers
The standard error for the sample mean exists
[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex].
How to find the standard error for the sample mean?Let the value of mean be [tex]$P(\bar{X} < 0.95)$$[/tex]
Normal Distribution, [tex]$\mu=1, \sigma=0.1, n=12$[/tex]
[tex]$P(\bar{X} < 0.95)=$[/tex] Area to the left of 0.95
we convert this to standard normal using
[tex]$z=\frac{\bar{x}-\mu_{\bar{x}}}{\sigma_{\bar{x}}}=\frac{\bar{x}-\mu}{\sigma / \sqrt{n}}$[/tex]
[tex]$z=\frac{0.95-(1)}{0.1 / \sqrt{12}} \approx-1.732051 \approx-1.73$[/tex]
[tex]$P(\bar{X}[/tex] < 0.95) = P(Z < -1.73) = 0.0418 (from z-table)
P(Z < -1.73); in a z-table having area to the left of z, locate -1.7 in the left most column. Move across the row to the right under column 0.03 and get value 0.0418.
[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex]
Therefore, the standard error for the sample mean exists
[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex].
The complete question is;
What is the probability that the sample mean will be below 0.95 centimeters?
At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken.
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What is the sign of 37+(-37)? Choose 1 answer: Positive Negative Neither positive nor negative the sum is zero
Answers
Mathematics. Sets Question. Answer Fast
Answers
Answer:
B
Step-by-step explanation:
the full domain is
(-∞,-7[ ∪ ]-7,+∞)
Mr. Anderson grows fruit which hesells at a farmers' market.- His truck has a total payloadcapacity (total weight ofpassengers and cargo) of1,200 pounds.- Mr. Anderson weighs 190 pounds.- The table he sells his fruit onweighs 10 pounds.- He transports his fruit in crates.Each crate weighs 3 pounds.- A crate can hold up to 22 poundsof fruit.Write and solve an equation to findC, the greatest number of fullcrates of fruit that Mr. Anderson cancarry in his truck along with himself and the table
Answers
We will have that the expression that represents the problem is:
[tex]1200>(3+22)C+190\Rightarrow1200>25C+190[/tex][tex]\Rightarrow1010>25C\Rightarrow C<40.4[/tex]So, at most he will be able to carry 40 crates with him.
> Question 1
In 2 to the 4th power = 16 number 2 is called what?
and number 4 is called what?
Answers
The most appropriate choice for exponents will be given by-
In [tex]2^4 = 16[/tex], 2 is called the base and 4 is called the power or index.
What is exponent?
Exponent of a number is the number of times a number is multiplied by itself.
For example: [tex]3^5 = 3 \times 3 \times 3 \times 3 \times 3[/tex], 3 is multiplied by itself 5 times
If [tex]a^m = a \times a \times a \times a .....[/tex](m times)
a is called the base and m is called the power or index,
Here,
In [tex]2^4 = 16[/tex], 2 is called the base and 4 is called the power or index.
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What values complete each statement?Enter your answers in the boxes.(16−−√)2 = in simplest form.By the Power of Power rule, (16 1/2)2=16 2/2. So, 16 1/2 must equal in radical form.
Answers
Box 1 )
[tex](\sqrt[]{16})^2=16[/tex]Box 2 )
[tex]16^{\frac{1}{2}}=\sqrt[]{16}[/tex]F(x) = 3 + 5x to the second power - x + 5, 2f(3-) - f(4) =
Answers
the given equation is
[tex]f(x)=3x^2-x+5[/tex]calculate f(-3) by putting x = -3
[tex]\begin{gathered} f(-3)=3(-3)^2-(-3)+5 \\ f(-3)=27+3+5=35 \\ \end{gathered}[/tex]now, f(4)
[tex]\begin{gathered} f(4)=3(4)^2-4+5 \\ f(4)=48+1=49 \end{gathered}[/tex]now the final calculation
[tex]\begin{gathered} 2f(-3)-f(4) \\ 2\times35-49 \\ 70-49 \end{gathered}[/tex]that is 70 -49 = 21
so the correct answer is 21
2f(-3) - f(4) = 21 .
In triangle JKL, tan(b°) = 3/4 and sin(b°) = 3/5 If triangle JKL is dilated by a scale factor of 3, what is cos(bº)?
Answers
ANSWER
cos(bº) = 4/5
EXPLANATION
When a triangle is dilated, the resulting triangle is similar to the original triangle. Therefore, the interior angles of the dilated triangle are congruent to the interior angles of the original triangle. This means that cos(bº) is the same for both triangles.
Using the relationship between these three trigonometric ratios:
[tex]\tan (bº)=\frac{\sin (bº)}{\cos (bº)}[/tex]We can find the cosine:
[tex]\cos (bº)=\frac{\sin (bº)}{\tan (bº)}[/tex][tex]\cos (bº)=\frac{\frac{3}{5}}{\frac{3}{4}}=\frac{3}{5}\colon\frac{3}{4}=\frac{3}{5}\times\frac{4}{3}=\frac{4}{5}[/tex]Please explain this to me
Answers
If a perpendicular b and b parallel to c, then the value of x = 8
Here b and c are parallel lines
The parallel lines are two lines in the same plane that are at equal distance from each other and that do not intersect at any point
Then a is perpendicular to b
The perpendicular lines are the line that forms the angle of 90 degrees for both angles
Therefore the given angles are 90 degrees
9x+18 = 90
9x = 90-18
9x = 72
x = 72/9
x = 8
Hence, If a perpendicular b and b parallel to c, then the value of x = 8
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The measure of three angels of a triangle are 43, 70, and x what is the value of x
Answers
According to the given data we have the following:
measure of three angels of a triangle are 43, 70, x
x?
The sum of the measures of the three angles of the triangle is 180
Therefore, to calculate the value of x we would have to make the following calculation:
43 + 70 + x = 180
113+ x=180
x=180-113
x=67
Therefore, the value of the angle of x would be 67
what variable expression should you subtract from both sides of the equation so that you are left with no variables on the right hand side
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
What variable expression should you subtract from both sides of the equation so that you are left with no variables on the right-hand side?
The variable expression is: subtract 5x from both sides so that you are left with no variables on the right-hand side
[tex]\begin{gathered} 6x\text{ - 10 = 5x + 15} \\ \text{Subtract 5 x from both sides, we have that:} \\ 6x\text{ - 5x - 10 = 5x - 5x + 15} \\ x\text{ - 10 = 15} \\ \text{Now, add 10 to both sides, we have that:} \\ x\text{ - 10 + 10 = 15 + 10} \\ x\text{ = 25} \\ \text{check:} \\ 6x\text{ - 10 = 5x + 15} \\ \sin ce,\text{ x = 25 , we have that:} \\ 6(25)\text{ - 10 = 5(25) + 15 } \\ 150\text{ - 10 = 125+ 15= 140 ( COR}\R ECT) \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]x\text{ = 25}[/tex]
100 POINTS ANSWER CORRECTLY PLS
Answers
Answer:
1.) y = -3/4x +2
2.) y = x - 4
3.) y = 2/3x - 4
4.) y = -1/2x + 5
5.) y = 8/3x +5
Step-by-step explanation:
1.)
Parallel means that the slopes will be the same.
So, m = -3/4
To find the equation, we must first use point-slope form.
[tex]y-y_{1} =m(x-x_{1} )[/tex]
y-(-1) = -3/4(x-4)
Now we clean this up and solve for y to get the answer in slope intercept form.
y+1= -3/4x + 3 => y = -3/4x +2
2.)
Perpendicular means that the slope is the negative reciprocal of the slope of the first line.
So, m = 1 as the negative reciprocal of -1 is +1.
Once again, we use point-slope form and the clean it up and solve for y to get the answer in slope-intercept form.
y - (-3) = 1(x-1) => y + 3 = x-1 => y = x - 4
3.)
Similar to the previous one, but with slope m = 2/3 (negative reciprocal)
y - (-4) = 2/3 (x - 0) => y + 4 = 2/3x => y = 2/3x - 4
4.)
Similar to the previous one, but with slope m = -1/2 (negative reciprocal)
y - 4 = -1/2(x-2) => y - 4 = -1/2x +1 => y = -1/2x + 5
5.)
Similar to the previous one, but with slope m = 8/3 (negative reciprocal)
y - (-3) = 8/3(x - (-3)) => y + 3 = 8/3x +8 => y = 8/3x +5
In one classroom homework is worth 25% of the final grade, each of the three projects is worth 10%, and the final exam is worth 45%. If student has an 87 on a homework average and a 94 on the first project, what is the students grade at this point if that same student from part a gets a 71 on the second project and a 78 on the third project what is the lowest grade the student can get on the final exam to get an 80 over on the course
Answers
Answer
• a) 30.9
,• b) 76
Explanation
Given
• Homework: 25%
,• Project: 10% (each)
,• Final exam: 45%
A student has:
Part A
• Homework: 86
,• First project: 94
Part B
• Second project: 71
,• Third project: 78
,• Total grade: 80
Procedure
• a)
To know the student's grade at the point where he has an 86 homework average and 94 on the first project. We have to multiply the ponderation of each category times the grade to find the final grade (TG), meaning:
[tex]TG=86(0.25)+94(0.10)[/tex]Simplifying:
[tex]TG=21.5+9.4[/tex][tex]TG=30.9[/tex]• b)
Following the same procedure, now we have to multiply the ponderations of the new grades, as follows:
[tex]TG=FE+30.9+71\cdot(0.1)+78\cdot(0.1)[/tex][tex]TG=FE+30.9+7.1+7.8[/tex][tex]TG=FE+45.8[/tex]Next, as we are asked to find the calculations of the grade of the exam to get a final grade of 80, we have to consider the latter and the ponderation for the exam:
[tex]80=x\cdot0.45+45.8[/tex]where x is the grade of the exam.
Solving for x:
[tex]x=\frac{80-45.8}{0.45}[/tex][tex]x=76[/tex]In January 1, Juan weighed 247 pounds and decided to diet and exercise. Kn June 30, Juan weighed 221 pounds. Determine the percent decrease in Juans weight from January 1 to June 30.
Answers
Given the initial value, w1, and the final value, w2, the percent decrease can be calculated as:
[tex]P=\frac{w_1-w_2}{w_1}\times100\%[/tex]The initial value is 247 and the final one is 221, so:
[tex]\begin{gathered} P=\frac{247-221}{247}\times100\% \\ P=\frac{26}{247}\times100\% \\ P=0.10526\ldots\times100\% \\ P\approx10.53\% \end{gathered}[/tex]So, the percent decrease is approximately 10.53%.
The mode of data 33, 22, 10, 0, 33, 40, 33 is _____
Answers
33,23,10,0,33,40,33
Mode of the data is 33
•The most repeated observation is known as Mode , here 33 is repeated 3 times while rest occur only once ! Hence the mode of the given data is 33.
Other info:-
•Mean = Sum of all observation/No.of Observations
Help please. Catching up on missed work from being out due to medical issues. Thank you in advance!
Answers
Let B be the number of cups of boiling water that we should mix with I cups of ice to get 3 cups of 110°F water.
Therefore, we can set the following equation:
[tex]\begin{gathered} B+I=3, \\ 220B+32I=110\cdot3. \end{gathered}[/tex]Subtracting B from the first equation we get:
[tex]\begin{gathered} B+I-B=3-B, \\ I=3-B\text{.} \end{gathered}[/tex]Substituting the above equation in the second one we get:
[tex]220B+32(3-B)=330.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} 220B+96-32B=330, \\ 188B+96=330. \end{gathered}[/tex]Subtracting 96 to the above equation we get:
[tex]\begin{gathered} 188B+96-96=330-96, \\ 188B=234. \end{gathered}[/tex]Dividing the above equation by 188 we get:
[tex]\begin{gathered} \frac{188B}{188}=\frac{234}{188}, \\ B\approx1.24. \end{gathered}[/tex]Substituting B=1.24 at I=3-B we get:
[tex]I=3-1.24=1.76.[/tex]Answer:
[tex]\begin{gathered} 1.26\text{ cups of boiling water.} \\ 1.74\text{ cups of ice.} \end{gathered}[/tex]
Consider the function f(x) = (x+4)(x+2), Dilate f(x) by x to create a new function of a higher degree,
a. Write the dilation of f(x) as g(x).
b. Sketch the graph of g(x).
c. identify the zeros of the graph of the function g(x)
Answers
The dilated function g(x) will be g(x) = x(x + 4)(x + 2). The zeroes of function g(x) = x(x + 4)(x + 2) will be x = 0, x = - 4, x = -2. The graph of the function g(x) is attached.
What is scale factor? How it is used in Dilating coordinates?Scale factor is used to compare 2 quantities, indicating by how much one quantity is greater than the other. It is denoted by K. Mathematically-
K = a/b.
If a coordinate point (x, y) is dilated by a scale factor of [k], then the coordinate point after dilation will be - (kx, ky).
Given is the function -
f(x) = (x+4)(x+2)
[A] -
For dilating the given f(x) by [x] times -
g(x) = [tex]x[/tex] f(x)
g(x) = x(x + 4)(x + 2)
Therefore, the dilated function g(x) will be -
g(x) = x(x + 4)(x + 2)
[B] -
The graph of the function g(x) is attached with the answer.
[C] -
The points where the graph of g(x) touches or cuts the x - axis, will represent the zeroes of the function g(x) = x(x + 4)(x + 2). It can be seen that the points are -
x = 0
x = - 4
x = - 2
The zeroes of function g(x) = x(x + 4)(x + 2) will be x = 0, x = - 4, x = -2.
Therefore, the dilated function g(x) will be g(x) = x(x + 4)(x + 2). The zeroes of function g(x) = x(x + 4)(x + 2) will be x = 0, x = - 4, x = -2. The graph of the function g(x) is attached.
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Timothy Tools is a company that produces hand-crafted hammers and wrenches. The following equations can be used to determine how many hammers the company can produce each day if x people are making hammers
Answers
The domain of the function of the equation cannot include zero because h(0) is not real.
A scale used to weigh objects is analogous to an equation. When the two pans are filled to the same level with anything, the scale will balance and the weights will be considered to be equal (such as grain).
To keep the balance in check, whenever any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. In general, if the same operation is carried out on both sides of an equation, the equation remains in balance.Equations that involve one or more functions and their derivatives are known as differential equations. By locating a derivative-free formulation for the function, they can be resolved.The equation is given as [tex]h(x) = \sqrt{2x^2+5x+3}[/tex]
The equation at x=0 given
h(0) = √(0+0-3)
or, h(0) = √(-3) which is an imaginary number
Therefore for the equation the value of x at 0 is undefined.
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Please help me on my assignment The ? Options are x and y
Answers
x, x
1.7
[tex]\lbrack1,7\rbrack[/tex]Explanation
Step 1
we can see in the graph, that :
the solutions of the equation f(x)=0, are the values where y =0 , it is when the line crosses the x-axis, so the solution of the first blank is
x
Step 2
and, the solution of the inequality
[tex]f(x)>0[/tex]is the set of values wich the graph is above the x-axis
Step 3
now, for the next question, let's check the points where the line crosses the x-axis, and the intervals where the lines is above the x-axis
we can see the solution of f(X)=0 are
[tex]\begin{gathered} x=1\text{ and x=7} \\ so \\ Input\text{ in the blank} \\ 1,7 \end{gathered}[/tex]Finally, check the interval where the graph is above the x-axis, it is from a to 7, in interval notation
[tex]\lbrack1,7\rbrack[/tex]
I hope this helps you
suppose that 18 inches of wire cost 72 cents. using the same rate how much in cents will 36 inches cost?
Answers
True or false? In deductive thinking, you start with a given set of rules and cinditions and determine what must be true as a consequence
Answers
In deductive thinking, you start with a given set of rules and conditions and determine what must be true as a consequence - True
In deductive thinking, conclusions are reached based on premises that are typically taken to be true. A conclusion is based on the concordance of several premises typically presumed to be true in this logical procedure. Top-down logic is another name for deductive thinking. It only makes use of data that is believed to be reliable. It excludes sentiments, feelings, and unsupported assumptions because it is challenging to assess the integrity of this data.
Making logical assumptions and basing a conclusion on them are the foundations of deductive thinking. It enables the individual to combine the information from two or more assertions to arrive at a sound conclusion. If something is presumptively true and a different object is connected to the first presumption, then the original truth must also apply to the second. Therefore, In deductive thinking, if you start with a given set of rules and conditions and determine what must be true as a consequence holds true.
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Are the triangles congruent using AAS?
True
False
Answers
Answer: True
Step-by-step explanation:
If you look both triangles have the same angles, so that means that they are congruent.