Answer: You are correct. The answer is choice C.
The sum of the vectors is the resultant vector, which is where the net force is directed.
An example would be if you had a ball rolling on a table and you bumped the ball perpendicular to its initial velocity, then the ball would move at a diagonal angle rather than move straight in the direction where you bumped it.
Acceleration is the change in velocity over time, so the acceleration vector tells us how the velocity's direction is changing.
The direction of the acceleration on a body upon which multiple forces are applied depends on the direction of the netforce acting on the body.
When multiple forces acts on a body, such that the different forces acts in different directions. The acceleration will be in the direction of the netforce. This is the direction where the Cummulative sum of the forces is greatest. Acceleration due to gravity is always acting downward, if the upward force is greater than the Gravitational force, then the acceleration won't be in that direction.Therefore, acceleration will be due in the direction of the netforce.
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Find the most general antiderivative of the function. (Use C for the constant of the antiderivative).
f(x) = 6x5 − 7x4 − 9x2
F(x) = ?
Answer:
[tex]x^6 - \frac{7x^5}{5} - 3x^3 + C[/tex]
will give 5 stars and thanks for correct answer Richard starts high school every day at 7:45 A.M.. How many seconds is Richard in school each day of school dismissed at 2:15 P.M.
A circle has center (3, -5) and the point (-1, -8) lies on the circumference of the circle. What is the equation of the circle in Standard Form?
Answer:
[tex] {(x - 3)}^{2} + {(y + 5)}^{2} = {5}^{2} [/tex]
Step-by-step explanation:
First find the radius
Which is the distance between the 2 points.
Radius =5
The answer in the standad form is above.
The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25
The standard equation of a circle is given as:
(x - a)² + (y - b)² = r²
where (a, b) is the center of the circle and r is the radius of the circle.
Given the center as (3, -5) hence the radius of the circle is the distance between (3, -5) and (-1, -8). Hence:
[tex]Radius=\sqrt{(-8-(-5))^2+(-1-3)^2} \\\\Radius=5\ units\\[/tex]
hence:
(x - 3)² + (y - (-5))² = 5²
(x - 3)² + (y + 5)² = 25
The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25
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If you invest $ 30 , 700 with an annual interest rate of 8.9 % , compounded daily, how much would you have at the end of 4 years?
Answer: $43,823.37
Step-by-step explanation:
Formula to calculate the accumulated amount earned on principal (P) at rate of interest (r) compounded daily after t years :
[tex]A=P(1+\dfrac{r}{365})^{365t}[/tex]
As per given , we have
P= $ 30,700
r= 8.9 % = 0.089
t= 4 years
[tex]A=30700(1+\dfrac{0.089}{365})^{365(4)}\\\\=30700(1+0.0002438)^{365(4)}\\\\=30700(1.0002438)^{1460}\\\\=30700(1.42747138525)\\\\=43823.3715272\approx43823.37[/tex]
Hence, the amount at the end of 4 years would be $43,823.37 .
In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of and a standard deviation of . Complete parts (a) through (d) below. (a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than . The probability of a student scoring less than is nothing. (Round to four decimal places as needed.) (b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between and . The probability of a student scoring between and is nothing. (Round to four decimal places as needed.) (c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than . The probability of a student scoring more than is nothing. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. than 0.05. B. than 0.05. C. The event in part is unusual because its probability is less than 0.05. D. The events in parts are unusual because its probabilities are less than 0.05.
The question is incomplete. Here is the complete question.
In a recent year, the socres for the reading portion of a test were normally distributed, with a mean of 23.3 and a standard deviation of 6.4. Complete parts (a) through (d) below.
(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 18. (Round to 4 decimal places as needed.)
(b) Find a probability that a random selected high school student who took the reading portion of the test has a score that is between 19.9 and 26.7.
(c) Find a probability that a random selected high school student who took the reading portion of the test ahs a score that is more than 36.4.
(d) Identify any unusual events. Explain your reasoning.
Answer: (a) P(X<18) = 0.2033
(b) P(19.9<X<26.7) = 0.4505
(c) P(X>36.4) = 0.0202
(d) Unusual event: P(X>36.4)
Step-by-step explanation: First, determine the z-score by calculating:
[tex]z = \frac{x-\mu}{\sigma}[/tex]
Then, use z-score table to determine the values.
(a) x = 18
[tex]z = \frac{18-23.3}{6.4}[/tex]
z = -0.83
P(X<18) = P(z< -0.83)
P(X<18) = 0.2033
(b) x=19.9 and x=26.7
[tex]z = \frac{19.9-23.3}{6.4}[/tex]
z = -0.67
[tex]z = \frac{26.7-23.3}{6.4}[/tex]
z = 0.53
P(19.9<X<26.7) = P(z<0.53) - P(z< -0.67)
P(19.9<X<26.7) = 0.7019 - 0.2514
P(19.9<X<26.7) = 0.4505
(c) x=36.4
[tex]z = \frac{36.4-23.3}{6.4}[/tex]
z = 2.05
P(X>36.4) = P(z>2.05) = 1 - P(z<2.05)
P(X>36.4) = 1 - 0.9798
P(X>36.4) = 0.0202
(d) Events are unusual if probability is less than 5% or 0.05. So, part (c) has an unusual event.
The probability will be:
(a) 0.2038
(b) 0.4046
(c) 0.0203
(d) Event in part (c) is unusual.
According to the question,
[tex]\mu = 23.2[/tex][tex]\sigma = 6.4[/tex]Let,
"X" shows the test scores.(a)
The z-score for X=18 will be:
→ [tex]z = \frac{X- \mu}{\sigma}[/tex]
[tex]= \frac{18-23.3}{6.4}[/tex]
[tex]= -0.828[/tex]
So,
The probability will be:
→ [tex]P(X<18) = P(z < -0.828)[/tex]
[tex]= 0.2038[/tex]
(b)
The z-score for X=19.9 will be:
→ [tex]z = \frac{X -\mu}{\sigma}[/tex]
[tex]= \frac{19.9-23.3}{6.4}[/tex]
[tex]= -0.531[/tex]
The z-score for X=26.7 will be:
→ [tex]z = \frac{X -\mu}{\sigma}[/tex]
[tex]= \frac{26.7-23.3}{6.4}[/tex]
[tex]= 0.531[/tex]
So,
The probability will be:
→ [tex]P(19.9 < X< 23.3) = P(-0.531 < z< 0.531)[/tex]
[tex]= 0.4046[/tex]
(c)
The z-score for X=36.4 will be:
→ [tex]z = \frac{X -\mu}{\sigma}[/tex]
[tex]= \frac{36.4-23.3}{6.4}[/tex]
[tex]= 2.047[/tex]
So,
The probability will be:
→ [tex]P(X > 36.4 )= P(z > 2.047)[/tex]
[tex]= 0.0203[/tex]
(d)
Just because it's probability value is less than 0.05, so that the events is "part c" is unusual.
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Expand $(x+1)(x^{2}+1)(x-1)$. What is the sum of the coefficients of the resulting expression?
Answer:
0
Step-by-step explanation:
Hello, please consider the following.
For any a and b real numbers we can write.
[tex](a-b)(a+b)=a^2-b^2[/tex]
We apply this formula two times here, as below.
[tex](x+1)(x^{2}+1)(x-1)=(x+1)(x-1)(x^{2}+1)\\\\=(x^2-1^2)(x^2+1)=(x^2-1)(x^2+1)\\\\=(x^2)^2-1^2=x^4-1[/tex]
We have the coefficient of 1 for [tex]x^4[/tex] and the constant term is -1, so the sum of the coefficients is 0.
Thank you.
Answer:
1
Step-by-step explanation:
(x + 1)(x² + 1)(x - 1)
= (x³ + x + x² + 1)(x - 1)
= x^4 - x³ + x² - x - x³ - x² + x - 1
= x^4 - 1
Coefficient of x^4 = 1
Suppose P( A) = 0.60, P( B) = 0.85, and A and B are independent. The probability of the complement of the event ( A and B) is: a. .4 × .15 = .060 b. 0.40 + .15 = .55 c. 1 − (.40 + .15) = .45 d. 1 − (.6 × .85) = .490
Answer: a. 0.4 × 0.15 = 0.060
Step-by-step explanation: Probability of the complement of an event is the one that is not part of the event.
For P(A):
P(A') = 1 - 0.6
P(A') = 0.4
For P(B):
P(B') = 1 - 0.85
P(B') = 0.15
To determine probability of A' and B':
P(A' and B') = P(A')*P(B')
P(A' and B') = 0.4*0.15
P(A' and B') = 0.06
Probability of the complement of the event is 0.060
There are three commercial tax-preparation offices in City A. The local Better Business Bureau has been receiving some complaints that one of the offices does not understand tax law well enough to provide expert advice. The Better Business Bureau has decided to invest several hundred dollars in grant money to test the claim. It has selected four people at random and has asked that they allow each of the offices to prepare their taxes using the same information. The following data show the tax bills ($1,000s) as figured by each office. The following data show the tax bills as figured by each office. The data are also located in the CD-ROM file Tax-test.Return Office 1 Office 2 Office 31 4376.20 5100.10 4988.032 5678.45 6234.23 5489.233 2341.78 2242.60 2121.904 9875.33 10300.30 9845.605 7650.20 8002.90 7590.886 1324.80 1450.90 1356.89Required:Use the ANOVA procedure on your calculator for completely randomized designs to determine whether there is a significant difference in the mean taxes due on tax returns?
Answer:
I have not answer
plz follow me....
Find the solution set of the inequality and what is the number? 16x − 7 ≤ − 71 A. C. ≤ D. ≥ E. =
x ≤ − 4
Step-by-step explanation:
Answer:
x ≤ -4
Step-by-step explanation:
16x − 7 ≤ − 71
Add 7 to both sides.
16x ≤ -64
Divide both sides by 16.
x ≤ -4
How to evaluate this help me out so lost?
Answer:
5443
Step-by-step explanation:
Order of Operations: BPEMDAS
Always left to right.
Step 1: Add 68 and 5042
68 + 5042 = 5110
Step 2: Add 5110 and 333
5110 + 333 = 5443
And we have our answer!
a=5,and 5+z=14,so a+z=14
Answer:
Z=9
Step-by-step explanation:
Insert A into A+Z=14
5+z=14
Subtract 5 on both sides, to find Z.
-5 -5
z=9
What is the range of g?
Answer:
R: {y∈R | -1 ≤ y ≤ 5}
Step-by-step explanation:
the lowest point is -1 and the highest point is 5.
Simplify the expression (6^4)^2
When raising a power inside parentheses to another power, multiply the numbers:
(6^4)^2 = 6^(4x2) = 6^8
Simplified = 6^8
6^8 = 1679616
Answer:
[tex] \boxed{ \purple{ {6}^{8} }}[/tex]Step-by-step explanation:
[tex] \mathsf{ ( { {6}^{4}) }^{2} }[/tex]
It is the example of Power to power law of indices.
Multiply the exponents
⇒[tex] \mathsf{ {6}^{4 \times 2} }[/tex]
Multiply the numbers
⇒[tex] \mathsf{ {6}^{8} }[/tex]
-------------------------------------------------------
[tex] \mathsf{\orange{ \underline{ power \: to \: power \: law \: of \: indices}}}[/tex]
If [tex] \mathsf{ ({x}^{a} )^{b}} [/tex] is an algebraic term then [tex] \mathsf{( {x}^{a} ) ^{b} = {x}^{a \times b} }[/tex]
i.e When an algebraic term in the index form is raised to another index , the base is raised to the power of two indices.
Hope I helped!
Best regards!!
Beginning 177 miles directly north of the city of Morristown, a van travels due west. If the van is travelling at a speed of 31 miles per hour, determine the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles. (Do not include units in your answer, and round to the nearest hundredth.)
Answer:
Step-by-step explanation:
From the given information;
let the hypotenuse be a , the opposite which is the north direction be b and the west direction which is the adjacent be c
SO, using the Pythagoras theorem
a² = c² + 177²
By taking the differentiation of both sides with respect to time t , we have
[tex]2a \dfrac{da}{dt} = 2c \dfrac{dc}{dt} + 0[/tex]
[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]
At c = 71 miles,[tex]a = \sqrt{ (71)^2 +(177)^2}[/tex]
[tex]a = \sqrt{ 5041+31329}[/tex]
[tex]a = \sqrt{ 36370}[/tex]
a = 190.71
SImilarly, [tex]\dfrac{dc}{dt} = \ 31 miles \ / hr[/tex]
Thus, the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles can be calculate as:
[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]
[tex]\dfrac{da}{dt} = \dfrac{71}{190.71} \times 31[/tex]
[tex]\dfrac{da}{dt} = 0.37229 \times 31[/tex]
[tex]\mathbf{\dfrac{da}{dt} = 11.54}[/tex] to the nearest hundredth.
Please give me the answer ASAP The average of 5 numbers is 7. If one of the five numbers is removed, the average of the four remaining numbers is 6. What is the value of the number that was removed Show Your Work
Answer:
The removed number is 11.
Step-by-step explanation:
Given that the average of 5 numbers is 7. So you have to find the total values of 5 numbers :
[tex]let \: x = total \: values[/tex]
[tex] \frac{x}{5} = 7[/tex]
[tex]x = 7 \times 5[/tex]
[tex]x = 35[/tex]
Assuming that the total values of 5 numbers is 35. Next, we have to find the removed number :
[tex]let \: y = removed \: number[/tex]
[tex] \frac{35 - y}{4} = 6[/tex]
[tex]35 - y = 6 \times 4[/tex]
[tex]35 - y = 24[/tex]
[tex]35 - 24 = y[/tex]
[tex]y = 11[/tex]
Okay, let's slightly generalize this
Average of [tex]n[/tex] numbers is [tex]a[/tex]
and then [tex]r[/tex] numbers are removed, and you're asked to find the sum of these [tex]r[/tex] numbers.
Solution:
If average of [tex]n[/tex] numbers is [tex]a[/tex] then the sum of all these numbers is [tex]n\cdot a[/tex]
Now we remove [tex]r[/tex] numbers, so we're left with [tex](n-r)[/tex] numbers. and their. average will be [tex]{\text{sum of these } (n-r) \text{ numbers} \over (n-r)}[/tex] let's call this new average [tex] a^{\prime}[/tex]
For simplicity, say, sum of these [tex]r[/tex] numbers, which are removed is denoted by [tex]x[/tex] .
so the new average is [tex]\frac{\text{Sum of } n \text{ numbers} - x}{n-r}=a^{\prime}[/tex]
or, [tex] \frac{n\cdot a -x}{n-r}=a^{\prime}[/tex]
Simplify the equation, and solve for [tex]x[/tex] to get,
[tex] x= n\cdot a -a^{\prime}(n-r)=n(a-a^{\prime})+ra^{\prime}[/tex]
Hope you understand it :)
The cost in dollars y of producing x computer
desks is given by y = 40x + 4000
X
100
200
300
a. Complete the table
y
b. Find the number of computer desks that can be produced for $6200. (Hint: Find x when y = 6200.)
a. Complete the table.
х
100
200
300
y
b. For $6200,_ computer desks can be produced
Answer:
a.
y= 40x +4000
x= 100 --> y= 40(100)+4000= 4000+4000=8000
x=200 --> y= 40(200)+4000= 6000+4000= 10000
x=300 --> y= 40(300)+4000= 12000+4000= 16000
(in $)
b.
y= 40x+4000
6200= 40x+4000
6200-4000= 40x
2200= 40x
2200/40= x
55= x
(in unit)
Step-by-step explanation:
I hope this helps
if u have question let me know in comments ^_^
At the beginning of March, a store bought a fancy watch at a cost of $250 and marked it up 20%. At the end of the month, the fancy watch had not sold, so the store marked it down 10%. What was the discounted price?
Answer:
$270
Step-by-step explanation:
Price after markup was 1.20($250) = $300
Price after discounting: (1.00 - 0.10)($300) = $270
Question 3 Rewrite in simplest rational exponent form √x • 4√x. Show each step of your process.
Answer:
4x
Step-by-step explanation:
Given:
√x • 4√x
Required:
Simplify in rational exponent form
SOLUTION:
Recall => [tex] \sqrt{a} = a^{\frac{1}{2}} [/tex]
Thus,
[tex] \sqrt{x}*4\sqrt{x} [/tex] can be expressed in exponent form as [tex] x^{\frac{1}{2}}*4x^{\frac{1}{2} [/tex]
When multiplying 2 bases having exponents together, their exponents should be added together, while you multiply the bases. I.e. [tex]x^m*x^n = x^{m+n }[/tex]
[tex] = x*4^{\frac{1}{2}+\frac{1}{2} [/tex]
[tex] = 4x^{1} = 4x [/tex]
The answer is 4x
Determine if the process appears to be within statistical control. If not, state the reason why not.
a. It does not appear to be within statistical control because there is an upward shift.
b. It appears to be within statistical control.
c. It does not appear to be within statistical control because there is an upward trend.
d. It does not appear to be within statistical control because there is increasing variation.
Answer:
c. It does not appear to be within statistical control because there is an upward trend.
Step-by-step explanation:
Statistical process control is a method for quality control which employs statistical method to monitor and control process. It ensures operation efficiency and ensuring required specification to reduce wastes in production lines. Here the process variation is out of control because the statistical control has an upward trend.
Will mark Brainliest! Which point is a vertex of the hyperbola?
A. (1,−15)
B. (1,−2)
C. (1,3)
D. (1,11)
Answer:
So (1,3) is a vertex (out of two) of the hyperbola.
Step-by-step explanation:
The vertices are marked by the dot on the hyperbola.
They are (1,3) and (1,-7).
However, (1,-7) is not on the list of answer choices, but (1,3) is.
So (1,3) is a vertex (out of two) of the hyperbola.
So (1,3) is a vertex (out of two) of the hyperbola.
What is hyperbola?a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant : a curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the cone.
According to the question
The vertices are marked by the dot on the hyperbola.
They are (1,3) and (1,-7).
However, (1,-7) is not on the list of answer choices, but (1,3) is.
Hence , (1,3) is a vertex (out of two) of the hyperbola.
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Use a t-test to test the claim about the population mean at the given level of significance using the given sample statistics. Assume the population is normally distributed.
Claim: μ ≥8 300, α = 0.10
Sample statistics: x = 8000, s = 440, n = 24
A. What are the null and alternative hypotheses?
B. What is the value of the standardized test statistic?
C. What is the p-value?
D. Decide whether to reject or fail to reject the null hypothesis.
Answer:
A
The null hypothesis is [tex]H_o : \mu \ge 8300[/tex]
The alternative hypothesis is [tex]H_a : \mu < 8300[/tex]
B
[tex]t = -3.34[/tex]
C
[tex]p-value = P(t< -3.34) = 0.00041889[/tex]
D
reject the null hypothesis
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 8300[/tex]
The sample mean is [tex]\ = x = 8000[/tex]
The standard deviation is [tex]s = 440[/tex]
The sample size is [tex]n = 24[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu \ge 8300[/tex]
The alternative hypothesis is [tex]H_a : \mu < 8300[/tex]
The test statistic is mathematically evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{8000- 8300 }{ \frac{440}{\sqrt{24} } }[/tex]
=> [tex]t = -3.34[/tex]
The p-value is obtained from the z -table ( reference calculator dot net ) , the value is
[tex]p-value = P(t< -3.34) = 0.00041889[/tex]
Looking at the values of [tex]p-value and \ \alpha[/tex] we see that [tex]p-value < \alpha[/tex] Hence we reject the null hypothesis
Convert 6 feet to miles ( round five decimal places
Answer:
0.00114
Step-by-step explanation:
Divide length value by 5280
A manager wants to determine an appropriate learning percentage for processing insurance claims for storm damage. Toward that end, times have been recorded for completion of each of the first six repetitions:
Repetition 1 2 3 4 5 6
Time (minutes) 46 39 35 33 32 30
a. Determine the approximate learning percentage. (Round your answer to the nearest whole percent. Omit the "%" sign in your response.)
P %
b. Using your answer from part a, estimate the average completion time per repetition assuming a total of 30 repetitions are planned. (Round your answer to 3 decimal places.)
Answer:
Step-by-step explanation:
The approximate learning percentage can be estimated by using a doubling method.
If we breakdown the repetitions into three consecutive parts, we have:
1 - 2
2 - 4
3 - 6
then
1 - 2 → 46P = 39
P =39/46
P = 0.8478
P = 84.8%
2 - 4 → 39P = 33
P = 33/39
P = 0.84615
P = 84.6%
3 - 6 → 35P = 30
P = 30/35
P = 0.8571
P = 85.7%
The average value of P = (84.8 + 84.6 + 85.7)/3 = 85.03%
[tex]\simeq[/tex] 85%
From the tables of Learning Curves coefficient
The values are likened against times derived from 85% table factors at T[tex]_1[/tex] = 46
Unit 1 2 3 4 5 6
Date 46 39 35 33 32 30
Computed - 39.1 35.56 33.26 31.56 30.22
b. Using your answer from part a, estimate the average completion time per repetition assuming a total of 30 repetitions are planned. (Round your answer to 3 decimal places.)
The average completion time = [tex]\mathtt{\dfrac{T_1 \times \ Total \ time\ factor}{n}}[/tex]
At the total time factor 30, from the learning curves table , n(30) = 17.091
Thus:
The average completion time = [tex]\mathtt{\dfrac{46 \times \ 17.091}{30}}[/tex]
The average completion time = [tex]\mathtt{\dfrac{786.186}{30}}[/tex]
The average completion time = [tex]\mathtt{26.2062}[/tex]
Which rule describes this transformation? (Zoom in to see it clearly)
Answer:
(x,y) -> (x+6, y-3)
Step-by-step explanation:
I followed c and it translated like the last ans choice.
Consider these five values a population: 7, 4, 6, 4, and 7. Determine the mean of the population. (Round your answer to 1 decimal place.)
Answer:
[tex]Mean = 5.6[/tex]
Step-by-step explanation:
Given
[tex]7,4,6,4,7[/tex]
Required
Determine the mean
Mean is calculated as thus;
[tex]Mean = \frac{\sum x}{n}[/tex]
Where n is the number of observation;
In this case;
[tex]n = 5[/tex]
and [tex]\sum x[/tex] is the sum of the observations
The expression becomes
[tex]Mean = \frac{7+4+6+4+7}{5}[/tex]
[tex]Mean = \frac{28}{5}[/tex]
[tex]Mean = 5.6[/tex]
Hence, the mean of the population is 5.6
I don’t understand this, may I get some help?
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80,023 written in scientific notation is [tex]8,0023[/tex] x [tex]10^4[/tex].
Step 1
To find a, take the number and move a decimal place to the right one position.
Original Number: 80,023
New Number: 8.0023
Step 2
New Number: 8 . 0 0 2 3
Decimal Count: 1 2 3 4
Now, to find b, count how many places to the right of the decimal.
There are 4 places to the right of the decimal place.
Step 3
Building upon what we know above, we can now reconstruct the number into scientific notation.
Remember, the notation is: a x 10^b
a = 8.0023
b = 4
Now the whole thing:
8.0023 x 104
Step 4
Check your work:
10^4 = 10,000 x 8.0023 = 80,023
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Have a great day/night!
❀*May*❀
Please help. I’ll mark you as brainliest if correct!
Answer:
The system is dependent:
x=-3t-7
y=-5t-15
z=t
Step-by-step explanation:
I chose to use a matrix to solve this system of equations. Once put into matrix form, you need to row reduce the system into its simplest form (Row Reduced Echelon form). Doing this, we find that the system is dependent on the z variable. And following usual procedures, we let z equal some other letter; which is t in this case. Then we isolate each variable to get the answer.
Check the attachment for the work.
[The arrows indicate a row swap and the parenthesis indicates addition if a constant multiple of one row to another]
A right triangle has the following vertices Find the area of the triangle
(7,-3) (4,-3) (4,9)
20 pnts
Answer:
Area = 18 square units
Step-by-step explanation:
To find the area of the triangle, let's go through the following steps:
(i) Let the vertices be;
A = (7, -3)
B = (4, -3)
C = (4, 9)
(ii) The sides of the triangle are therefore,
AB, BC and CA
(iii) Using the distance formula, calculate the lengths of AB, BC and CA
[tex]AB = \sqrt{(7-4)^2 + ( -3 - (-3))^2}[/tex]
[tex]AB = \sqrt{3^2 + (0)^2}\\[/tex]
[tex]AB = \sqrt{9}[/tex]
[tex]AB = 3[/tex]
[tex]BC = \sqrt{(4-4)^2 + ( -3 - 9)^2}[/tex]
[tex]BC = \sqrt{0^2 + (-12)^2}[/tex]
[tex]BC = \sqrt{144}[/tex]
[tex]BC = 12[/tex]
[tex]CA = \sqrt{(4-7)^2 + ( 9 - (-3))^2}[/tex]
[tex]CA = \sqrt{(-3)^2 + (12)^2}[/tex]
[tex]CA = \sqrt{9 + 144}[/tex]
[tex]CA = \sqrt{153}[/tex]
[tex]CA = 12.4[/tex]
(iv) Now that we have all the sides, let's calculate the area of the triangle using the Heron's formula.
Area = [tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex]
Where;
p = [tex]\frac{a + b + c}{2}[/tex]
a, b and c are the sides of the triangle.
In our case,
let
a = AB = 3
b = BC = 12
c = CA = 12.4
∴ p = [tex]\frac{3 + 12 + 12.4}{2}[/tex]
p = 13.7
Area = [tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex]
Area = [tex]\sqrt{13.7(13.7-3)(13.7-12)(13.7-12.4)}[/tex]
Area = [tex]\sqrt{13.7(10.7)(1.7)(1.3)}[/tex]
Area = [tex]\sqrt{323.9639}[/tex]
Area = 17.999
Area = 18 square units
OR
To get the area of the triangle, we can use a much simpler approach.
Since the triangle is a right triangle,
(i) the hypotenuse, which is the longest side is CA = 12.4
(ii) the other two sides are AB and BC. These two sides will form the right angle.
Therefore, we can use the relation:
Area = [tex]\frac{1}{2}[/tex] x base x height
Where;
the base or height can either be AB or BC
Area = [tex]\frac{1}{2}[/tex] x 3 x 12
Area = 18 square units
PS: In a right triangle, the other two sides apart from the hypotenuse form the right angle.
Complete the table of values for y=-x^2+2x+1
X -3, -2, -1,0,1,2,3,4,5
Y -14,7, ,1, -2 -14
Answer:
see the attachment
Step-by-step explanation:
When you have a number of function evaluations to do, it is convenient to let a graphing calculator or spreadsheet do them. That avoids the tedium and the mistakes in arithmetic.
Here's your completed table.
Find the measure of a.
A. 60
B. 57
C. 40
D. 80
Answer:
Option (C)
Step-by-step explanation:
Since angle 'a' is the inscribed angle of the given triangle
Therefore, angle measure of the intercepted arc will be equal to the double of the inscribed angle.
x = 2a ⇒ a = [tex]\frac{x}{2}[/tex]
By the tangent-chord theorem,
"Angle between a chord and tangent measure the half of the angle measure of intercepted minor arc"
[tex]\frac{x}{2}[/tex] = 40°
Therefore, a = [tex]\frac{x}{2}[/tex] = 40°
Option (C) will be the answer.
