Answer:
[tex]slope = \dfrac{-680}{9}[/tex]
Step-by-step explanation:
We are given coordinates of two points:
Let the points be A and B respectively:
[tex]A(\dfrac{7}{20}, \dfrac{8}{3})\\B(\dfrac{3}{8}, \dfrac{7}{9})[/tex]
To find the slope of line AB.
Formula for slope of a line passing through two points with coordinates [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:
[tex]m = \dfrac{y_2- y_1}{x_2- x_1}[/tex]
Here, we have:
[tex]x_2 = \dfrac{3}{8}\\x_1 = \dfrac{7}{20}\\y_2 = \dfrac{7}{9}\\y_1 = \dfrac{8}{3}\\[/tex]
Putting the values in formula:
[tex]m = \dfrac{\dfrac{7}{9}- \dfrac{8}{3}}{\dfrac{3}{8}- \dfrac{7}{20}}\\\Rightarrow m = \dfrac{\dfrac{7-24}{9}}{\dfrac{15-14}{40}}\\\Rightarrow m = \dfrac{\dfrac{-17}{9}}{\dfrac{1}{40}}\\\Rightarrow m = \dfrac{-17\times 40}{9}\\\Rightarrow m = \dfrac{-680}{9}[/tex]
So, the slope of line AB passing through the given coordinates is:
[tex]m = \dfrac{-680}{9}[/tex]
PLSSSSSSS HELP WILL MARK BRAINLIEST Doug owns a lawn mowing and landscaping business. The income from the business is given by the function f(x) = 2x + 54, where f(x) is the income in dollars and x is the area in square meters of lawn mowed. If he has earned {204, 344, 450, 482} dollars in the last four months, what are the corresponding areas of lawn he mowed?
Answer:
i think this person answered but idrk perseusharrison79
Step-by-step explanation:
For 2 parallelograms, the corresponding side lengths are 1 inch and x inches, and 2 inches and 6 inches.
Not drawn to scale
StartFraction 1 over x EndFraction = StartFraction 2 over 6 EndFraction
StartFraction 1 over x EndFraction = StartFraction 6 over 2 EndFraction
StartFraction 1 over 6 EndFraction = StartFraction 2 over x EndFraction
One-half = StartFraction 6 over x EndFraction
Step-by-step explanation:
Someone please answer this emergency pleaseee
Answer:
7). y = 140
8). x = 9
Step-by-step explanation:
Question (7).
All-right pencil factory will produce the graphite pencils, table formed will represent a linear graph.
Three points on the graph are (12, 42) and (18, 63), (40, y)
Slope of the line passing through these points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{63-42}{18-12}[/tex] = [tex]\frac{y-42}{40-12}[/tex]
[tex]\frac{21}{6}[/tex] = [tex]\frac{y-42}{40-12}[/tex]
3.5 = [tex]\frac{y-42}{40-12}[/tex]
98 = y - 42
y = 140
Question (8),
If a bicyclist rides at a constant rate, table formed will represent a linear graph.
Slope of a line passing through three points (2, 25), (5, 62.5) and (x, 112.5) given in the table,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{62.5-25}{5-2}=\frac{112.5-62.5}{x-5}[/tex]
[tex]\frac{37.5}{3}=\frac{50}{x-5}[/tex]
37.5x - 187.5 = 150
37.5x = 337.5
x = 9
find the third angle in a triangle when the other two angles are (2a-32)° and (3a+22)°
Answer:
(190-5a)°
Step-by-step explanation:
Sum of internal angles of a triangle equals to 180°
If the third angle is x, then we have:
(2a-32)°+(3a+22)° +x = 180°(5a- 10)° +x= 180°x= (180+10-5a)°x= (190-5a)°The third angle is: (190-5a)°
CAN SOMEONE PLEASE HELP ME THIS IS DUE SOON!!
Answer:
95 ft²
Step-by-step explanation:
Given:
regular pyramid with,
Square base of side length (s) = 5 ft
Slant height (l) = 7 ft
Required:
Surface area
Solution:
Surface area of a regular pyramid = ½*P*l + B
Where,
P = perimeter of the square base = 4(s) = 4(5) = 20 ft
l = slant height = 7 ft
B = area of base = s² = 5² = 25 ft²
Surface area = ½*20*7 + 25
= 10*7 + 25
= 70 + 25
Surface area of regular pyramid = 95 ft²
solve the inequality:8x+3>2x-15
8x + 3 > 2x - 15
8x - 2x > -15 - 3
6x > -18
x > -3
Answer:
x > -3
Step-by-step explanation:
8x + 3 > 2x - 15
Add -3 and -2x on both sides.
8x - 2x > -15 - 3
6x > -18
Divide 6 into both sides.
x > -18/6
x > -3
7 + x - 15 = -2.67 solve for x
Answer:
5.33
Step-by-step explanation:
Move your numbers so that they're separate from the variables. You should now have x = -2.67 + 8; x = 5.33
Answer:
x=5.33
Step-by-step explanation:
7+x-15=-2.67
7-15+x=-2.67
Add 7 and -15
-8+x=-2.67
Add 8 on both sides
which equal to 5.33
x=5.33
The mean arrival rate of flights at Philadelphia International Airport is 195 flights or less per hour with a historical standard deviation of 13 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days, the arrival rate per day is given in the data vector below called flights. Air traffic control manager wants to test if there is sufficient evidence that arrival rate has increased.
flights <- c(210, 215, 200, 189, 200, 213, 202, 181, 197, 199,
193, 209, 215, 192, 179, 196, 225, 199, 196, 210,
199, 188, 174, 176, 202, 195, 195, 208, 222, 221)
a) Find sample mean and sample standard deviation of arrival rate using R functions mean() and sd().
b) Is this a left-tailed, right-tailed or two-tailed test? Formulate the null and alternative hypothesis.
c) What is the statistical decision at the significance level α = .01?
Answer:
a) The sample mean is M=200.
The sample standard deviation is s=13.19.
b) Right-tailed. The null and alternative hypothesis are:
[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]
c) At a significance level of 0.01, there is notenough evidence to support the claim that the arrival rate is significantly higher than 195.
Step-by-step explanation:
We start by calculating the sample and standard deviation.
The sample size is n=30.
The sample mean is M=200.
The sample standard deviation is s=13.19.
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{30}(210+215+200+. . .+221)\\\\\\M=\dfrac{6000}{30}\\\\\\M=200\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{29}((210-200)^2+(215-200)^2+(200-200)^2+. . . +(221-200)^2)}\\\\\\s=\sqrt{\dfrac{5048}{29}}\\\\\\s=\sqrt{174.07}=13.19\\\\\\[/tex]
This is a hypothesis test for the population mean.
The claim is that the arrival rate is significantly higher than 195. As we are interested in only the higher tail for a significant effect, this is a right-tailed test.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]
The significance level is 0.01.
The standard deviation of the population is known and has a value of σ=13.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{13}{\sqrt{30}}=2.373[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{200-195}{2.373}=\dfrac{5}{2.373}=2.107[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>2.107)=0.018[/tex]
As the P-value (0.018) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is notenough evidence to support the claim that the arrival rate is significantly higher than 195.
How many x-intercepts does the graph of y = 2x2 + 4x - 3 have?
Answer:
3
Step-by-step explanation:
Given
y
=
2
x
2
−
4
x
+
3
The y-intercept is the value of
y
when
x
=
0
XXX
y
=
2
(
0
)
2
−
4
(
0
)
+
3
=
3
For a quadratic in the general form:
XXX
y
=
a
x
2
+
b
x
+
c
the determinant
Δ
=
b
2
−
4
a
c
indicates the number of zeros.
Δ
⎧
⎪
⎨
⎪
⎩
<
0
==⇒
no solutions
=
0
==⇒
one solution
>
0
==⇒
two solutions
In this case
XXX
Δ
=
(
−
4
)
2
−
4
(
2
)
(
3
)
<
0
so there are no solutions (i.e. no values for which the expression is equal to zero).
This can also be seen from a graph of this equation:
graph{2x^2-4x+3 [-6.66, 13.34, -0.64, 9.36]}
Answer link
Vinícius Ferraz
Nov 13, 2015
(
0
,
3
)
Explanation:
x
=
0
⇒
y
=
0
−
0
+
3
y
=
0
⇒
x
=
−
b
±
√
b
2
−
4
a
c
2
a
a
=
2
,
b
=
−
4
,
c
=
3
But
Δ
< 0, then there is no real root
(
x
0
,
0
)
.
Answer:
it has 2
Step-by-step explanation:
I hope this helps!
It is believed that 11% of all Americans are left-handed. In a random sample of 100 students from a particular college with 10123 students, 14 were left-handed. Find a 98% confidence interval for the percentage of all students at this particular college who are left-handed.
Answer:
Step-by-step explanation:
We can calculate this confidence interval using the population proportion calculation. To do this we must find p' and q'
Where p' = 14/100= 0.14 (no of left handed sample promotion)
q' = 1-p' = 1-0.14= 0.86
Since the requested confidence level is CL = 0.98, then α = 1 – CL = 1 – 0.98 = 0.02/2= 0.01, z (0.01) = 2.326
Using p' - z alpha √(p'q'/n) for the lower interval - 0.14-2.326√(0.14*0.86/100)
= -2.186√0.00325
= -2.186*0.057
= 12.46%
Using p' + z alpha √(p'q'/n)
0.14+2.326√(0.14*0.86/100)
= 0.466*0.057
= 26.5%
Thus we estimate with 98% confidence that between 12% and 27% of all Americans are left handed.
Which could be the side lengths of a triangle? (A) 2,2,4 (B) 3,4,7 (C) 4,5,8 (D) 5,5,10 (E) 7,3,10 PLEASE HELP
Answer:
(C) 4,5,8
Step-by-step explanation:
Since 4+5 = 9 and 9 is bigger than 8, that means that the side 8 can fit into the triangle without there being an open space.
Answer:
Option C { 4,5,8 }
Step-by-step explanation:
By the Triangle Inequality Theorem, the length of two sides together must be greater than the length of the remaining side. Respectively their difference must be less than the length of the another side.
* I like to memorize this concept by thinking about a door. The more you open the door, the greater the distance between the door and the wall - as they are proportional. That is how we concluded this theorem.
______
{ 2, 2, 4 } is our first option. The difference of 4 and 2 is equal to the remaining length, 2. { 3, 4, 7 } is not applicable as well, considering that the addition of 3 and 4 is equivalent to the length of the 3rd side, 7. However, the lengths { 4, 5,8 } have no such " errors. " It could be the side lengths of a possible triangle.
______
Solution = { 4,5,8 }
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two side
bf this triangle?
O 5 cm and 8 cm
O 6 cm and 7 cm
O 7 cm and 2 cm
8 cm and 9 cm
Answer:
It's (D) 8 cm and 9 cm. Hope this helps you!
Step-by-step explanation:
The other 2 sides added have to be greater than 13.
Answer:
8 and 9
Step-by-step explanation:
The triangle inequality states that the sum of the two shortest sides must be greater than the longest side.
Let's check the first one. 5 + 8 > 13 → 13 > 13 which is false.
6 + 7 > 13 → 13 > 13 which is false.
7 + 2 > 13 → 9 > 13 which is false.
8 + 9 > 13 → 17 > 13 which is true.
Jenna worked 13 hours more than Jose last month. If Jenna worked 9 hours for every 4 hours that Jose worked, how many hours did they each work?
The tens digit in a two digit number is 4 greater than one’s digit. If we interchange the digits in the number, we obtain a new number that, when added to the original number, results in the sum of 88. Find this number
Answer:
The original digit is 62
Step-by-step explanation:
Let the Tens be represented with T
Let the Units be represented with U
Given:
Unknown Two digit number
Required:
Determine the number
Since, it's a two digit number, then the number can be represented as;
[tex]T * 10 + U[/tex]
From the first sentence, we have that;
[tex]T = 4 + U[/tex]
[tex]T = 4+U[/tex]
Interchanging the digit, we have the new digit to be [tex]U * 10 + T[/tex]
So;
[tex](U * 10 + T) + (T * 10+ U) = 88[/tex]
[tex]10U + T + 10T + U= 88[/tex]
Collect Like Terms
[tex]10U + U + T + 10T = 88[/tex]
[tex]11U + 11T = 88[/tex]
Divide through by 11
[tex]U + T = 8[/tex]
Recall that [tex]T = 4+U[/tex]
[tex]U + T = 8[/tex] becomes
[tex]U + 4 + U = 8[/tex]
Collect like terms
[tex]U + U = 8 - 4[/tex]
[tex]2U = 4[/tex]
Divide both sides by 2
[tex]U = 2[/tex]
Substitute 2 for U in [tex]T = 4+U[/tex]
[tex]T = 4 + 2[/tex]
[tex]T = 6[/tex]
Recall that the original digit is [tex]T * 10 + U[/tex]
Substitute 6 for T and 2 for U
[tex]T * 10 + U[/tex]
[tex]6 * 10 + 2[/tex]
[tex]60 + 2[/tex]
[tex]62[/tex]
Hence, the original digit is 62
By about how much will f (x comma y comma z )equalsln StartRoot x squared plus y squared plus z squared EndRoot change if the point Upper P (x comma y comma z )moves from Upper P 0 (6 comma 4 comma 12 )a distance of dsequals0.1 unit in the direction of 3 Bold i plus 6 Bold j minus 2 Bold k?
Answer:
pls format
Step-by-step explanation:
Please answer this correctly
Answer:
1/7
Step-by-step explanation:
There are 7 cards, 1 of which is less than 2. Therefore, P (less then 2) = 1/7
Answer:
1/7
Step-by-step explanation:
The number from the list that is less than 2 is 1.
1 number out of a total of 7 numbers.
= 1/7
You spend $3.50 on fruit. Apples cost $0.20 each while oranges cost $0.30 each. The equation models the situation, where x is the number of apples and y is the number of oranges. Which of the following is not a possible solution in the context of the problem?
a. 1 apple; 11 oranges
b. 11 apples; 1 orange
c. 7 apples; 7 oranges
d. 4 apples; 9 oranges
Answer:
b. 11 apples; 1 orange
Step-by-step explanation:
We test each option, and see if the total is $3.50(what you spend). If the result is different, it is not a possible solution.
a. 1 apple; 11 oranges
1 apple for $0.20
11 oranges for $0.30 each
0.20 + 11*0.30 = $3.50
Possible solution
b. 11 apples; 1 orange
11 apples for $0.20 each
1 orange for $0.30
11*0.2 + 0.3 = 2.5
Not $3.5, so this is not a possible solution.
This is the answer
c. 7 apples; 7 oranges
7*0.2 + 7*0.3 = $3.5
Possible
d. 4 apples; 9 oranges
4*0.2 + 9*0.3 = $3.5
Possible
A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen, resulting in the accompanying data (from "Engineering Properties of Soil," Soil Science, 1998: 93–102).1.10 5.09 0.97 1.59 4.60 0.32 0.55 1.450.14 4.47 1.20 3.50 5.02 4.67 5.22 2.693.98 3.17 3.03 2.21 0.69 4.47 3.31 1.170.76 1.17 1.57 2.62 1.66 2.05The values of the sample mean, sample standard deviation,and (estimated) standard error of the mean are2.481, 1.616, and .295, respectively. Does this data suggestthat the true average percentage of organic matterin such soil is something other than 3%? Carry out atest of the appropriate hypotheses at significance level.10. Would your conclusion be different if a 5 .05 hadbeen used? [Note: A normal probability plot of the datashows an acceptable pattern in light of the reasonablylarge sample size.]
Answer:
We conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.
We conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.
Step-by-step explanation:
We are given a random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen;
1.10, 5.09, 0.97, 1.59, 4.60, 0.32, 0.55, 1.45, 0.14, 4.47, 1.20, 3.50, 5.02, 4.67, 5.22, 2.69, 3.98, 3.17, 3.03, 2.21, 0.69, 4.47, 3.31, 1.17, 0.76, 1.17, 1.57, 2.62, 1.66, 2.05.
Let [tex]\mu[/tex] = true average percentage of organic matter
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 3% {means that the true average percentage of organic matter in such soil is 3%}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu \neq[/tex] 3% {means that the true average percentage of organic matter in such soil is something other than 3%}
The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean percentage of organic matter = 2.481%
s = sample standard deviation = 1.616%
n = sample of soil specimens = 30
So, the test statistics = [tex]\frac{2.481-3}{\frac{1.616}{\sqrt{30} } }[/tex] ~ [tex]t_2_9[/tex]
= -1.76
The value of t-test statistics is -1.76.
(a) Now, at 10% level of significance the t table gives a critical value of -1.699 and 1.699 at 29 degrees of freedom for the two-tailed test.
Since the value of our test statistics doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.
(b) Now, at 5% level of significance the t table gives a critical value of -2.045 and 2.045 at 29 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.
Find the domain of the function f(x) = 7x2 + 8x - 15.
Answer:
Domain is all real numbers or (negative infinity, positive infinity)
Step-by-step explanation:
Domain is all values of x (inputs) that will work with the function. Since a parabola has no limits for x, and all numbers work for x, then the domain can be any number. That leaves us with All Real Numbers as our answer.
I have no idea what this is
Answer:
B. -1.
Step-by-step explanation:
[tex]i^1[/tex] = i
[tex]i^2 = -1[/tex]
[tex]i^3 = -i[/tex]
[tex]i^4 = 1[/tex]
...And it keeps going in a pattern, from i to -1 to -i to 1. And so, we have four values.
34 / 4 = 8 with a remainder of 2. That means that the value of [tex]i^{34}[/tex] is the same thing as [tex]i^2\\[/tex], so it is B. -1.
Hope this helps!
PLEASE HELP!!!! Find the common difference
Answer:
The common difference is 1/2
Step-by-step explanation:
Data obtained from the question include:
3rd term (a3) = 0
Common difference (d) =.?
From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:
a7 – 2a4 = 1
Recall:
a7 = a + 6d
a4 = a + 3d
a3 = a + 2d
Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.
But, a3 = 0
a3 = a + 2d
0 = a + 2d
Rearrange
a = – 2d
Now:
a7 – 2a4 = 1
Substituting the value of a7 and a4, we have
a + 6d – 2(a + 3d) = 1
Sustitute the value of 'a' i.e –2d into the above equation, we have:
–2d + 6d – 2(–2d + 3d) = 1
4d –2(d) = 1
4d –2d = 1
2d = 1
Divide both side by 2
d = 1/2
Therefore, the common difference is 1/2
***Check:
d = 1/2
a = –2d = –2 x 1/2 = –1
a3 = 0
a3 = a + 2d
0 = –1 + 2(1/2)
0 = –1 + 1
0 = 0
a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2
a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2
= (–2 + 3)/2 = 1/2
a7 – 2a4 = 1
2 – 2(1/2 = 1
2 – 1 = 1
1 = 1
HELP!! Im not sure what i did wrong!!
I'm not sure what exactly you did wrong, but I agree with you that the sample size is too small, so the correct answer will probably be the fourth options. Hope that this gives you some confidence, and 'm sorry not to be able to help you any further...
Of 41 bank customers depositing a check, 22 received some cash back. Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (Round your answers to 4 decimal places.)
Answer:
CI: {0.4085; 0.6647}
Step-by-step explanation:
The confidence interval for a proportion (p) is given by:
[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]
Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:
[tex]p=\frac{22}{41}=0.536585[/tex]
Thus the confidence interval is:
[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]
The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}
Simplify 4 + (−3 − 8)
Answer:
-7
Step-by-step explanation:
4 + (−3 − 8)
PEMDAS
Parentheses first
4 + (-11)
Add and subtract next
-7
Answer:
first I'm using BODMAS
4+(-11)
= -7
hope it helps
what value of x is in the solution set of 2(3x–1)>4x–6?
Answer:
x > -2
Step-by-step explanation:
2(3x–1)>4x–6
Divide each side by 2
2/2(3x–1)>4x/2–6/2
3x-1 > 2x-3
Subtract 2x from each side
3x-2x-1 > 2x-3-2x
x-1 > -3
Add 1 to each side
x-1+1 > -3+1
x > -2
1- if angle A = 30, then its complementary is -- and its supplementary is
2- If a triangle has an area of 360, and its base = 10, what is its height?
3- if two triangles have the same angle measures, then the triangles are
4. What is the definition of similar triangles?
5- One of triangle congruence tests is SSS, what are 3 other congruent tests
6- What is a regular polygon?
7- If a rectangle has an area of 240 and a length of 24, what is the width?
8- Colinear points lie on the same
9- 3 non-colinear points determine a
10- The sum of 2 supplementary angles add up to -------
1 - complementary = 90- 30 = 60
suplementary = 180- 30 = 150
2 - area = hb/2 = 360 = hb/2 = h = 72
3 - similar
4- see number 3
5 - asa, ssa, sas
6 - polygon that had all equal angle measures and sides (equiangular and equilateral)
7 - length x width = area so
240 / 24 = 10
8 - line
9 - triangle
10 - 180, as see in question 1
vote me brainliest ):>
HELP! will give brainlest or whatever its called... Triangle ABC has vertices A(–2, 3), B(0, 3), and C(–1, –1). Find the coordinates of the image after a reflection over the x-axis. A’ B’ C’
Answers:
A ' = (-2, -3)
B ' = (0, -3)
C ' = (-1, 1)
=======================================================
Explanation:
To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.
Algebraically, the reflection rule used can be written as [tex](x,y) \to (x,-y)[/tex]
Applying this rule to the three given points will mean....
Point A = (-2, 3) becomes A ' = (-2, -3)Point B = (0, 3) becomes B ' = (0, -3)Point C = (-1, -1) becomes C ' = (-1, 1)The diagram is provided below.
Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.
Answer:
(-2,-3)...(0,-3)...(-1,1)
Step-by-step explanation:
Find the sum. Please
Answer:
[tex]\dfrac{2y^2 +12y -8}{y^3-3y+2}[/tex]
Step-by-step explanation:
It usually works to factor the denominators, so you can determine the least common denominator.
[tex]\dfrac{2y}{y^2-2y+1}+\dfrac{8}{y^2+y-2}=\dfrac{2y}{(y-1)^2}+\dfrac{8}{(y-1)(y+2)}\\\\=\dfrac{2y(y+2)}{(y-1)^2(y+2)}+\dfrac{8(y-1)}{(y-1)^2(y+2)}=\dfrac{2y^2+4y+8y-8}{(y-1)^2(y+2)}\\\\=\boxed{\dfrac{2y^2 +12y -8}{y^3-3y+2}}[/tex]
I travelled at 60km/h and took 2 hours for a certain journey. How long would it have taken me if I had travelled at 50km/h?
Answer:
2 hours and 24 minutes
Step-by-step explanation:
2 hours at 60 km/h means you have travelled 2*60=120 km
120 km at 50 km/h takes 120/50 = 2.4 hours
2.4 hours is 2 hours and 0.4*60 = 24 minutes.
Mexican currency is the peso. One Mexican peso is currently equal to 0.055 U.S. dollars. If a traveler exchanges $400 for Mexican pesos, how many pesos will he receive? Round to the nearest peso.
Answer:
7,273 Pesos
Step-by-step explanation:
1 Peso = $0.055
The formula below converts pesos to dollars:
1 Peso x 0.055 = $1
The formula below converts dollars to pesos:
$1/0.055= 1 Pesos
We use the second formula because we are coverting
from dollars to pesos.
$400/0.055=7,273 Pesos
Answer:
22
Step-by-step explanation:
If one Mexican peso is .055 U.S dollars that means it has a greater value than the dollar so we can make the following ratio 1:.055. But if the .055 is a 400 1:400 we just multiply to get 22.
Which expression is equivalent to [tex]4^7*4^{-5}[/tex]? A. [tex]4^{12}[/tex] B. [tex]4^2[/tex] C. [tex]4^{-2}[/tex] D. [tex]4^{-35}[/tex]
Answer:
B. [tex]4^2[/tex]
Step-by-step explanation:
[tex]4^7 \times 4^{-5}[/tex]
Apply rule (if bases are same) : [tex]a^b \times a^c = a^{b + c}[/tex]
[tex]4^{7 + -5}[/tex]
Add exponents.
[tex]=4^2[/tex]
Answer:
[tex] {4}^{2} [/tex]Step by step explanation
[tex] {4}^{7} \times {4}^{ - 5} [/tex]
Use product law of indices
i.e
[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]
( powers are added in multiplication of same base)
[tex] = {4}^{7 + ( - 5)} [/tex]
[tex] = {4}^{7 - 5} [/tex]
[tex] = {4}^{2} [/tex]
Hope this helps...
Best regards!