Answers
We are given the following equation that models the height of a ball:
[tex]h(t)=15t-4.9t^2[/tex]part a) is to find the distance traveled by the ball in the interval [1,3], to do that we replace the values of t=1 and t=2 in the equation, like this
[tex]\begin{gathered} h(1)=15(1)-4.9(1)^2=11 \\ h(3)=15(3)-4.9(3)^{2^{}}=0.9 \end{gathered}[/tex]The total distance is the difference between the two points, that is:
[tex]h(1)-h(3)=11-0.9=10.1[/tex]Related Questions
Hi guys.I was sick today and I’m still not feeling good.I missed out on class and I’ll be giving 25 points to whoever helps me.Thank you
Answers
5x + 2 + 5x - 2 = 180
5x = 180
x = 36
For the function, f(x) = -x + 4, find f(-2), f(-0.5) and f(3)
Answers
Given function is
[tex]f(x)=-x+4[/tex][tex]\begin{gathered} f(-2)=2+4=6 \\ f(-0.5)=0.5+4=4.5 \\ f(3)=-3+4=1 \end{gathered}[/tex]correct option is D 6, 4.5, 1.
Shelia is making a cake. She
needs 1/3 of a cup of oil. She
has 1/4 of a cup. How much
more does she need
Answers
She need 1/12 cup of oil. A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.
What is meant by fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. fraction, A number expressed as a quotient in arithmetic, in which a numerator is divided by a denominator. Both are integers in a simple fraction. A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction has a numerator that is less than the denominator. A fraction is a portion of a whole number and a method of dividing a number into equal parts.How to find how much cup she want?She needs 1/3 cup of oil She have 1/4 cup of oilTo find how much need to obtain 1/3 of cup
we need to subtract what we have from what we need.
so , we have 1/4 and need 1/3
= 1/3 - 1/4
= [tex]\frac{1 * 4}{3 * 4} - \frac{1 * 3}{4 * 3}[/tex]
= 1/12
she need 1/12 cup of oil more to make cake.
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Can anyone explain this for #30?
Answers
Q.29 Variance is S² = 17.33
Q.30 Variance is S² = 46.67
What is Variance ?
Variance is the expectation of the squared deviation of a random variable from its population mean or sample mean.
S² = ∑(x - x(bar) )² / (n - 1 )
S² = sample Variance
x = the value of the one observation
x(bar) = the mean value of all observation
n = the number of observation
Q.29 | x | (x -x(bar)) | (x - x(bar) )² |
| -------------------------------------- |
| 2 | -5 | 25 |
| 6 | -1 | 1 |
| 8 | 1 | 1 |
| 12 | 5 | 25 |
-------------------------------------------
| 28 | 0 | 52 |
----------------------------------------------
x(bar) means, x mean = ∑x
∑x = (2 + 6 + 8 + 12) / 4
= 28/4
= 7
Now, put the values in variance formula,
S² = ∑(x - x(bar) )² / (n - 1 )
= 52 / (4 -1)
= 52/ 3
= 17.33
Q.30 | x | (x -x(bar)) | (x - x(bar) )² |
| -------------------------------------- |
| 10 | -7 | 49 |
| 14 | -3 | 9 |
| 18 | 1 | 1 |
| 26 | 9 | 81 |
-------------------------------------------
| 68 | 0 | 140 |
----------------------------------------------
x(bar) means, x mean = ∑x
∑x = (10 + 14 + 18 + 26)/4
= 68/4
= 17
Now, put the values in variance formula,
S² = ∑(x - x(bar) )² / (n - 1 )
= 140 / (4 -1)
= 140 / 3
= 46.67
Therefore, the Variance of Q.29 is S² = 17.33
and, for Q.30 Variance is S² = 46.67
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pls guys need a quick hep
Factorise 2x³+9x²+7x-6=0
Answers
The most appropriate choice for factorization will be given by-
(x +2)(x + 3)(2x - 1) is the factorization of f(x) = 2x³+9x²+7x-6
x = -2, -3, [tex]\frac{1}{2}[/tex] are the solutions of f(x) = 0
What is factorization?
Factorization is the process of breaking down of an algebraic expression into product of algebraic expressions of smaller degree.
Each algebraic expression of smaller degree are called factors
Here,
Vanishing method will be used
f(x) = 2x³+9x²+7x-6
[tex]f(-2) = 2(-2)^3 + 9(-2)^2 + 7(-2) -6\\= -16 + 36 -14 -6\\ = 0[/tex]
(x + 2) is a factor of f(x)
[tex]f(x)[/tex] [tex]= 2x^2(x + 2) + 5x(x + 2) - 3(x + 2)[/tex]
[tex]= (x + 2)(2x^2 + 5x - 3) \\ = (x + 2)(2x^2 + 6x - x - 3) \\ = (x + 2)[2x(x + 3) - 1(x + 3)] \\ = (x + 2)(x + 3)(2x - 1)[/tex]
For solving f(x) = 0
x +2 = 0 or x + 3 = 0 or 2x - 1 = 0
x = -2 or x = -3 or x = [tex]\frac{1}{2}[/tex] are the solutions of f(x) = 0
This is the required factorization of f(x)
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Add or subtract the monomials. (Simplify your answer compl
2a²+6²-8a² + x²y - 3x + 9xy²
Answers
After simplification of the given monomial 2a²+6²-8a² + x²y - 3x + 9xy², the result is -6a²- 3x + x²y + 9xy² + 12.
What are monomials?A monomial in mathematics is essentially a polynomial with only one term. There are two possible definitions of a monomial: A monomial, also known as a power product, is a product of variables, possibly with repetitions, and powers of variables with nonnegative integer exponents. A polynomial with only one term is called a monomial. An algebraic expression known as a monomial typically has one term, but it can also have multiple variables and a higher degree. When 9 is the coefficient, x, y, and z are the variables, and 3 is the degree of the monomial, for instance, 9x³yz is a single term.So, 2a²+6²-8a² + x²y - 3x + 9xy²:
Now, simplify as follows:
2a²+6²-8a² + x²y - 3x + 9xy²2a²-8a²- 3x + x²y + 9xy² + 6²-6a²- 3x + x²y + 9xy² + 12Therefore, after simplification of the given monomial 2a²+6²-8a² + x²y - 3x + 9xy², the result is -6a²- 3x + x²y + 9xy² + 12.
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x - y ≥-3 and 3x + 2y ≥ 0
Answers
First, if we draw the lines of the equations x-y = -3 and 3x+2y = 0, we get the following:
the red line represents the first equation and the blue line represents the second equation. But since we are working with inequalities, the intersection between these two inequalities will be the intersection of the semiplanes that they form.
To check the region that will be the intersection, we can check two opposite points and see if both inequalities are true. In this case, if we take the points (-2,-2) and (2,2), we get the following:
[tex]\begin{gathered} -2-(-2)\ge-3\text{ and }3(-2)+2(-2)\ge0 \\ \Rightarrow0\ge3\text{ and }-10\ge0 \end{gathered}[/tex]notice that the second inequality is not true. Now, with the point (2,2), we get:
[tex]0=2-2\ge-3\text{ and }3(2)+2(2)\ge0[/tex]which are true, therefore, the region that represents both inequalities is the following:
The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 4 minutes and a standard deviation of 3 minutes.
Find the probability that it takes at least 6 minutes to find a parking space. (Round your answer to four decimal places.)
Answers
The probability that it takes at least 6 minutes to find a parking space is given as: 0.1587. See the explanation below.
What is probability?
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
The working of the above solution is given as follows:
Given:
Mean = 4 minutes
Standard deviation = 3 minutes
P(X < A) = P(Z < (A - mean) /standard deviation)
P(at least 6 minutes) = P(X≥6)
= 1 - P(X < 6)
= 1 - P(Z < (6 - 4)/2)
= 1 - P(Z < 1)
= 1 - 0.8413
P = 0.1587
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if you divide the age of the first President Bush when he was inaugurated by 2 and add 14 years you get the age of president Clinton when he was first inaugurated. how old was president G H.W. Bush when he was inaugurated?Age of first president Bush 54Age of Clinton 46
Answers
Let's call x the age of the first president bush, then:
Taking into account the sentence, "if you divide the age of the first President Bush when he was inaugurated by 2 and add 14 years you get the age of president Clinton when he was first inaugurated", we can write the following equation:
x/2 + 14 = 46
So, solving for x, we get:
x/2 = 46 - 14
x/2 = 32
x = 32*2
x = 64
Answer: The first president Bush was 64 years old when he was inaugurated.
help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
Answer: I think it is -5, but im not very sure srry
Step-by-step explanation:
Given g(x)=x^2-5x, find the equation of the secant line passing through (-3,g(-3)) and (4g(4)). Write your answer in form of y=mx+b
Answers
Given:
[tex]g(x)=x^2-5x\text{ ; (}-3,g(-3)),(4,g(4))[/tex][tex]g(-3)=(-3)^2-5(-3)[/tex][tex]g(-3)=9+15[/tex][tex]g(-3)=24[/tex][tex]g(4)=4^2-5(4)[/tex][tex]g(4)=16-20[/tex][tex]g(4)=-4[/tex]Equation of line with the points (-3,24) and (4,-4)
[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}[/tex][tex]\frac{y-24_{}}{-4_{}-24_{}}=\frac{x+3_{}}{4_{}+3_{}}[/tex][tex]\frac{y-24_{}}{-28_{}}=\frac{x+3_{}}{7_{}}[/tex][tex]\frac{y-24_{}}{-4_{}}=\frac{x+3_{}}{1_{}}[/tex][tex]y-24_{}_{}=-4(x+3)_{}_{}[/tex][tex]y_{}=-4x-12+24[/tex][tex]y=-4x+12[/tex]
75 - (5+2 (5) +7(8) +1)
Answers
Answer:
3
Step-by-step explanation:
75 - (5 + 10 + 56 + 1)
75 - (15 + 56 + 1)
75 - (71 + 1)
75 - 1 x 72
75 - 72
3
In a board game, students draw a number, do not replace it, and then draw asecond number. Determine the probability of each event occurring.
Answers
The probability P(choosing then an odd number, a 6) is 9 / 56
The figure of the board game is shown below.
From the question, we have
There are eight numbers on the board game.
Odd number total: (1, 9, 1) = 3
6 digits in total equal 3
Probability is "necessary outcome" divided by "all possible outcomes."
P = 3 / 8 (choosing an odd number).
without replacement
Board game numbers remaining: 8 - 1 = 7.
P(choosing a 6) = 3/7
Hence,
probability, P(choosing then an odd number, a 6) = 3/8 * 3/7 = 9 / 56
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
Complete question: In a board game, students draw a number do not replace it, and then draw a second number. Determine the probability of each event occurring. Drawing an odd number then drawing a 6? dependent events.
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One day in October at 9am, Taylor began hiking an 8-mile trail, hiking for 2.5 hours at a pace of 2 miles per hour, and then stopping for half an hour to enjoy the view and have a snack. Taylor then hiked the remainder of the trail at a speed of 3 miles per hour.
Later, Micah decided to run the same trail. Micah began 1.5 hours after Taylor began hiking, and ran at a rate of 7 miles per hour.
Will Micah catch up to Taylor? If so, when? If not, why not?
Answers
Using proportions, it is found that Micah caught up to Taylor at 11:06 AM.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using relations in the context of the problem.
For this problem, the relation between velocity, distance and time is used, that is, velocity equals distance divided by time, hence:
v = d/t.
Then the distance is:
d = vt.
For Taylor, his trail is divided in these following intervals:
5 miles in 2.5 hours = 5 miles at 11:30 am, as 2 x 2.5 = 5.Saw the view and had the snack until 12 am.Completed the trial at 1 pm, as he hiked the remaining 3 miles at the rate of 3 miles per hour.For Micah, the time that he took to complete the trail is:
t = d/v = 8/7 = 1.14 hours.
Hence he completed his trial around 11:40 AM, as he left at 10:30 A.M.
He caught up to Taylor during the first interval of his trip, when the motion functions are as follows:
Taylor: 2t + 3. (when Micah left at 10:30 A.M = 1.5 hours after Taylor, Taylor had already hiked 3 miles).Micah: 7t.Then:
7t = 2t + 3.
5t = 3.
t = 3/5.
t = 0.6 hours = 36 minutes after Micah left = 11:06 A.M.
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Hi, can you help me to solve this problem, please!!!
Answers
Given:
The equation of a parabola is given as,
[tex]y=x^2-5[/tex]The objective is to find the axis of symmetry of the parabola.
Explanation:
The general formula to find the axis of symmetry of a parabolic equation is,
[tex]x=-\frac{b}{2a}\text{ .. . . . . (1)}[/tex]From the given equation,
[tex]\begin{gathered} a=1 \\ b=0 \\ c=-5 \end{gathered}[/tex]On plugging the obtained values in equation (1),
[tex]\begin{gathered} x=-\frac{0}{2(1)} \\ x=0 \end{gathered}[/tex]Hence, the axis of symmetry of the parabola is at x = 0.
you want to buy some beans a 6 oz package cost $2.10 a 14 oz package cost $5.04 a 20 oz package cost $6.60
Answers
QUESTION:
you want to buy some beans a 6 oz package cost $2.10 a 14 oz package cost $5.04 a 20 oz package cost $6.60. Which package is the best to buy?
ANSWER
We will first find the unit price.
6 0z = $2.10
1 oz = $2.10/6 = $0.35
a 14 oz package that cost $5.04
14 0z = $5.04
1 oz = $5.04 / 10 = $0.504
a 20 oz package that cost $6.60
20 oz = $6.60
1 oz = $6.60 / 2 =$3.30
Comparing the three prices, the 6 oz package that cost $2.30 has the lowest price. This implies that it is the best to buy.
An experimental blood test has been developed for lockjaw by the National Institute of HealthDue to the experimental nature of the test, it is not 100% accurateIn a trial of the blood test, the following probabilities were computed 51% of the participants in the trial have lockjaw the participants with lockjaw, 76% have a positive blood test the participants who do not have lockjaw, 84% have a negative blood test Round your answers to three decimals a ) What is the probability that a random participant will have a negative blood test ? b ) If a randomly selected participant has a positive blood test , what is the probabi that they do not have lockjaw ?
Answers
The probabilities in the context of this problem are given as follows:
a) Negative blood test: 0.543 = 54.3%.
b) Do not have lockjaw, given that the test is positive: 0.1682 = 16.82%.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which the parameters of the formula are described as follows:
P(B|A) is the probability of event B happening, given that event A happened.[tex]P(A \cap B)[/tex] is the probability of both events A and B happening.P(A) is the probability of event A happening.For item a, the percentages associated with negative blood tests are given as follows:
84% of 49% (do not have lockjaw).24% of 51% (have lockjaw).Hence the probability is:
p = 0.84 x 0.49 + 0.24 x 0.51 = 0.534 = 53.4%.
For item b, the probabilities associated with positive blood tests and not having lockjaw are given as follows:
0.466 = 46.6% positive.16% of 49% have positive tests and do not have lockjaw.Hence the conditional probability is:
P(B|A) = 0.49 x 0.16/0.466 = 0.1682 = 16.82%.
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Round 3,204 to the nearest thousand
Answers
to round to the nearest thousand, we have to look at the hundreds place. In this case, there is a 2 in the hundreds place, which is less than 5. Then, the 3 in the thousands place must be kept. In conclusion, 3,204 rounded to the nearest thousand is 3,000
Answer:
3,000
Step-by-step explanation:
the thousands place is where the 3 is and we look at the number next to it if it is 5 or over we round up or if it’s under 5 we round down and since 2 is under 5 we round down to 3,000
The diameter of a circle is 20 inches. What is the radius, in inches, of the circle?
Answers
Given:
The diameter of a circle is 20 inches.
So, d = 20 inches
We will find the radius of the circle (r)
The diameter is two times the radius
Or, we can say, the radius is half of the diameter
so, r = d/2 = 20/2 = 10 inches
so, the answer will be The radius = 10 inches
Use the elimination method when solving the translated system Two angles are (complementary angles are angles whose sum is 90.) Their difference is 40. Find the angles. The larger angle is ? , and the smaller angle is ?.
Answers
Let's write the equation system first. We have two angles, let's call the, A and B, wich are complementary. This is:
[tex]A+B=90º[/tex]Also their difference is 40º:
[tex]A-B=40º[/tex]The system is;
[tex]\begin{cases}A+B=90º \\ A-B=40º\end{cases}[/tex]Now, if we add the two equations, since we have a "B" and a "-B", they will eliminate:
[tex]\begin{gathered} (A+B=90º)+(A-B=40º) \\ A+B+A-B=90º+40º \\ A+A+B-B=130º \\ 2A=130º \\ A=\frac{130º}{2}=65º \end{gathered}[/tex]The value of one of the angles is 65º. To find the other angle, we can go back to the first equation, A + B = 90º:
[tex]65º+B=90º[/tex]And solve:
[tex]B=90º-65º=25º[/tex]The larger angle is 65º and the smaller angle is 25º
Hi someone please help me and thanks have a great day. Hi someone please help me and thanks have a great day Question number 5Hi someone please help me and thanks have a great day.
Answers
Answer
a) Angle L = 36.9°
Angle N = 53.1°
b) For the relationship between them, we can see that
Angle L + Angle N = 36.9° + 53.1° = 90°
Hence, they both sum up to give 90° and are thus complementary angles.
Explanation
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
For this question, we first use Angle L as the non-right-angle angle
Hypotenuse = LN = 5
Opposite = NM = ?
Adjacent = LM = 4
Angle = L
Trignometric ratios allow us to interprete CAH as
Cos L = (Adj/Hyp)
Cos L = (4/5)
Cos L = 0.8
L = Cos⁻¹ (0.8)
L = 36.9°
Now, using Angle N as the non-right-angle angle,
Hypotenuse = LN = 5
Opposite = LM = 4
Adjacent = NM = ?
Angle = N
Trignometric ratios allow us to interprete SOH as
Sin N = (Opp/Hyp)
Sin N = (4/5)
Sin N = 0.8
N = Sin⁻¹ (0.8)
N = 53.1°
b) For the relationship between them, we can see that
Angle L + Angle N = 36.9° + 53.1° = 90°
Hence, they both sum up to give 90° and are thus complementary angles.
Hope this Helps!!!
Convert 7935 ml into litres
Answers
Answer:
7.935L
Step-by-step explanation:
1L=1000ml
7935/1000=7.935
Answer:
Step-by-step explanation:
1000 ml = 1 litre
7000 ml = 7 litres
935 ml = 0.935 litres
7935 ml = 7.935 litres
Hope this helped
The graph shown is the graph of which function?A. f(x)=tan xB. f(x)= sec xC. f(x)= csc xD. f(x)=cot x
Answers
The graph shown in the graph of f(x) = cot x. (Option D)
Ethan is measuring the lengths of various distances for a science project using feet. He is using the following formula to convert the distances to yards.
A. Proportional
B. Non- Proportional
C. Both Proportional and Non-Proportional
D. Neither Proportional nor Non-Proportional
Answers
Pete Size read the following partial advertisement: Price $20,999; down payment $1,000 cash or trade; $390.85 per month for 60 months. Calculate (A) the total finance charge and (B) the APR. (to the nearest percent).
Answers
The total finance charge is $3452 and the APR will be 6.45%.
How to calculate the value?The total finance charge will be:
Price = $20999
Down payment = $1000
Loan amount = $20999 - $1000 = $19999
Total repayment = $390.85 × 60 = $23451
Total finance charge = $23451 - $19999 = $3452
It should be noted that the APR will be:
= Rate(nper, pmt, -pv) × 12
where nper = 60
PMT = $390.85.
pv = 19999
APR = 6.45%
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Find the coordinates of the vertices of each
figure after the given
transformation.
reflection across y = -1
Answers
The x-components of the vertices are all that need to be taken into consideration for reflection along a vertical axis (x = -1).
How can coordinates be determined after reflection?The x-coordinates and y-coordinates move when a point is reflected across the line y = x. The line y = x reflects the point (x, y), and the reflection is (y, x).
The new value of x for any point (x, y) would be the angle 'd' with respect to the reflection axis (x -(-1)), then inverted for reflection around the reflection axis x = -1. x’ = -1 -d… where x = -1 -(x + 1) = -x -2 and d = (x - (-1)) = (x + 1)
For instance, if a = (1, 3), a' = (-1, -2, 3) = (-3, 3).
If you have a triangle with some vertices on one side and some on the other, straddling the axis, this reflection will still hold true for vertices on either side of the reflection axis.
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Find the PERIMETER of a square with sides 6 yards long. ANS.P = _______,
Answers
The given dimension of the square is 6 yards.
The perimeter of the square is express as : 4 x side
Perimeter of the square with the side 6 yards = 4 x 6
Perimeter of square = 24 yards
Answer. The perimeter of the square = 24yards
The unknown triangle ABC has angle A= 44º and sides a = 15 and c= 20. How many solutions are there for triangle?
Answers
Step 1: '
Find the sides and the angles.
Apply sine rule to find angle C
Step 2
[tex]\begin{gathered} \frac{a}{\sin A}\text{ = }\frac{c}{\sin C} \\ \frac{15}{\sin44}\text{ = }\frac{20}{\sin C} \\ \frac{15}{0.695}\text{ = }\frac{20}{\sin C} \\ \sin C\text{ = }\frac{20\times0.695}{15} \\ s\text{inC = 0.92666666} \\ C=sin^{-1}(0.9266666667) \\ C\text{ = 68} \end{gathered}[/tex]Step 3
44 +
Step 4
Find side b
[tex]\begin{gathered} \frac{a}{\sin A}\text{ = }\frac{b}{\sin B} \\ \frac{15}{\sin44}\text{ = }\frac{b}{\sin 68} \\ \frac{15}{0.695}\text{ = }\frac{b}{0.927} \\ b\text{ = }\frac{15\times0.927}{0.695} \\ b\text{ = 20} \end{gathered}[/tex]Final answer
Since angle C = angle B, the length of the sides must also be equal.
Hence,
0 triangle
In the triangle shown we can find the angle as follows.A153936(a) = sin-X(b) 0 - cos(C) 0 = tan-10
Answers
We need to calculate the three trigonometrics relations on the right triangle. They are as follow:
[tex]\begin{gathered} \sin \theta=\frac{36}{39}=0.92 \\ \cos \theta=\frac{15}{39}=0.38 \\ \tan \theta=\frac{36}{15}=2.4 \end{gathered}[/tex]We need to use this values on each option. The "sin^-1" is the inverse of the sine, the "cos^-1" is the inverse of the cosine and the "tan^-1" is the inverse of the tangent. If we use these values on the functions we will find the value of theta.
[tex]\sin ^{-1}0.92=\text{ 66.93}[/tex]The angle is equal to 66.93 degrees
Prove the following statement using the given pieces of information.2Given: ZGPS = ZJPS, PS_L_GJProve: ASJP – ASGPZGPS ZJPSbecause perpendicular lines form right angles, and all right anglès are congruent.PS and PS arethe two pairs of congruent angles.Click to select your answer(s).
Answers
Answer:
[tex]\measuredangle GPS=\measuredangle JPS[/tex]Because it is one of the given pieces of information.
[tex]\measuredangle PSG\cong\measuredangle PSJ[/tex]because perpendicular lines form right angles, and all right angles are congruent.
PS and PS are adjacent sides next to the two pairs of congruent angles.
[tex]PS\cong PS[/tex]By the Reflexive Property of Congruence
[tex]\Delta SJP\cong\Delta SGP[/tex]by ASA triangle congruence rule
Explanation:
Given the figure of the triangle in the attached image.
Given that;
[tex]\measuredangle GPS=\measuredangle JPS[/tex]Because it is one of the given pieces of information.
Then we can observe that;
[tex]\measuredangle PSG\cong\measuredangle PSJ[/tex]because perpendicular lines form right angles, and all right angles are congruent.
Also,
PS and PS are adjacent sides next to the two pairs of congruent angles.
And;
[tex]PS\cong PS[/tex]By the Reflexive Property of Congruence
Thus,
[tex]\Delta SJP\cong\Delta SGP[/tex]by ASA triangle congruence rule
