On one day a Plumber Joe earned $80 on a plumbing job. Out of his earnings he spent $6.85 on tea and snacks, $5.50 on food and $21.40 on tools. Before reaching home that evening his boss sent Plumber Joe $22 on "cash app", which his boss said was a tip from his early morning plumbing job. How much did he save on that day?

Answer:

Well none of the answers are correct as maximum height is found by doing -b/2a which gives the x coordinate of the vertex also known as the heighest or lowest point. But when plugged in it gives the lowest point assuming you made the mistake of making the 16 positive when its supposed to be negative you would plug it in and get 98 which isn't an answer choice assuming 34 is the ground when you subtract that you get 64 whch still isn't an answer choice check your numbers in the equation

Answer:

64 feet

Step-by-step explanation:

You can solve this by completing the square and turning the equation into that of a parabola, where the uppermost vertex is the highest point in the ball's flight path.

[tex]h=-16(t^2-4t+4)+98[/tex]

[tex]h=-16(t-2)^2+98[/tex]

Since the first term there is negative, the largest possible answer that you can get is if that term is 0. The only way to make it 0 is for t to be 2, so you know that that is when the highest point is. If the first term is 0, all that is left is 98, which is the highest height. However, since you initially start at 98, you only end up going 64 feet up (I guess C is the closest to that?). Hope this helps!

Answer:

P(blue) = 0.33

P(green) = 0.14

P(purple) = 0.24

P(yellow) = 0.29

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, we have that:

7+3+6+5 = 21 tils.

7 of them are blue. So

P(blue) = 7/21 = 0.33

3 of them are green. So

P(green) = 3/21 = 0.14

6 of them are yellow. So

P(yellow) = 6/21 = 0.29

5 of them are purple. So

P(purple) = 5/21 = 0.24

Answer:

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

According to the question

7 + 3 + 6 + 5 = 21 in a bag

[tex]P(blue) = \frac{7C_1}{21C_1} \\\\=\frac{7}{21} \\\\=\frac{1}{3} \\\\= 0.33[/tex]

[tex]P(green) = \frac{3C_1}{21C_1} \\\\= \frac{3}{21} \\\\=\frac{1}{7} \\\\= 0.14[/tex]

[tex]P(yellow)=\frac{6C_1}{21C_1} \\\\=\frac{6}{21}\\\\=\frac{2}{7} \\\\=0.29[/tex]

[tex]P(purple) = \frac{5C_1}{21C_1} \\\\=\frac{5}{21} \\\\=0.24[/tex]

Answer:

RS, RT and ST

Step-by-step explanation:

A tangent to a circle is a line that meets a circle at only one point.

AP is the radius and XT is not even a line.

Hope it helps!

Answer:

$0.34

Step-by-step explanation:

a = p*w

a = .06*5.65

a = 0.339

rounded = 0.34

hope this helps :)

Using the given formula T = LS

And given the time is 3 minutes (3 x 60 = 180 seconds)and the speed is 4-1/2 inches per second:

180 = L x 4-1/2

Solve for L by dividing both sides by 4-1/2:

L = 180 / 4-1/2

L = 40

The length should be 40 inches.

Final answer:

To record a 3-minute confession at 4 1/2 inches per second, an officer needs 810 inches of magnetic tape.

Explanation:

To determine how long of a tape a police officer needs to record a 3-minute confession at an operating speed of 4 1/2 inches per second, we use the formula T = L/S, where T is the time in seconds, L is the length of the tape in inches, and S is the operating speed in inches per second. First, convert the 3-minute confession time into seconds: 3 minutes × 60 seconds per minute = 180 seconds. Next, solve for L using L = T × S. Here, T = 180 seconds and S = 4.5 inches per second (since 1/2 inch is 0.5 inches). Thus, L = 180 × 4.5 = 810 inches. Therefore, the officer needs 810 inches of tape.

Therefore, as per the above explaination, the correct answer is 810 InchInches.

Answer:

C.

Step-by-step explanation:

In geometry, a vertex is the point where three or more edges meet on a shape (a 3-dimensional one of course). The other letters label sides or faces of the shape.

Answer:

C

Step-by-step explanation:

The easiest way to explain it is that A,B, and D are all labeling lines. A vertex is like a corner, with at least three lines protruding from it. A vertex is each angular point in a shape.

hope this helps :)

Answer:

b.) -2= -2

Step-by-step explanation:

i got it correct

Answer:

-2=-2

Step-by-step explanation:

Answer: i beleve it should be a

Step-by-step explanation:

The equation of the parabola f(x) = x² is transformed right 2, up 3, to make another parabola of the equation g(x) = (x - 2)² + 3. Hence, the first option is the right choice.

The process of modifying an existing graph, or graphed equation, to generate a version of the following graph is known as graph transformation.

If the equation of the original graph is f(x) and the transformed graph is g(x), such that g(x) = f(x + p) + q, then the graph of g(x) is p units left and q units up from f(x).

In the question, we are given the equations of the parabolas f(x) = x² and g(x) = (x - 2)² + 3, where f(x) is transformed to make g(x).

We are asked to identify the transformation from f(x) to g(x).

The equation of g(x) = (x - 2)² + 3, in terms of f(x) = x² can be written as

g(x) = f(x- 2) + 3, which is of the form g(x) = f(x + p) + q, where the graph of g(x) is transformed from f(x) by moving it p units left and q units right.

So, we can say that f(x) = x² is moved 2 units right and 3 units up to form g(x) = (x - 2)² + 3.

∴ The equation of the parabola f(x) = x² is transformed right 2, up 3, to make another parabola of the equation g(x) = (x - 2)² + 3. Hence, the first option is the right choice.

Learn more about the transformation of graphs at

https://brainly.com/question/1548871

#SPJ2

Answer:

C. 5 feet

Step-by-step explanation:

Answer:

5 foot 1 foot + 2 foot + 24 inches

Answer: The probability that the first coin will land heads up is : 50

               The probability that the second coin will land heads up is

               The probability that both coins will land heads up is : 25

Step-by-step explanation:

Answer: Both coins 1/4

First coin 1/2

Second coin 1/2

Answer:

18

Step-by-step explanation:

3(2)+2(4)+4=

6+8+4=18

The solution to the equation 3x + 2y + 4 when x = 2 and y = 4 is 18.

In the equation given, we are asked to find the value of 3x + 2y + 4 when x = 2 and y = 4.

First, let's substitute these values into the equation. We get 3×2 + 2×4 + 4, which simplifies to 6 + 8 + 4.

Adding these together gives us a total of 18. Therefore, the solution to the following equation is 18.

https://brainly.com/question/32789785

#SPJ2

Answer:

There are 27,720 ways to select the committee

Step-by-step explanation:

First, it is necessary to know how many ways are there to select 3 members, if there are 9 members of the mathematics department. This can be found using the following equation:

Where nCk gives as the number of ways in which we can select k elements from a group of n elements. So, replacing n by 9 and k by 3 members, we get:

So, there are 84 ways to select 3 members from 9 members of the mathematics department.

At the same way, we can calculate that there are 330 ways to select 4 members from the 11 that belong to the Computer science department as:

Finally the total number of ways in which we can form a committee with 3 faculty members from mathematics and 4 from the computer science department is calculated as:

9C3 * 11C4 = 84 * 330 = 27,720

Answer:

(x/4) +1 OR (4/x)+1

Step-by-step explanation:

Answer:

We conclude that the true mean weight is not 28.3 grams at 5% significance level.

Step-by-step explanation:

We are given that some students checked 6 bags of Doritos marked with a net weight of 28.3 grams.

They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5. The average weight is 29.0 and the standard deviation is 0.36.

Let [tex]\mu[/tex] = true mean weight of bag.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 28.3 grams     {means that the true mean weight is 28.3 grams}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 28.3 grams     {means that the true mean weight is not 28.3 grams}

The test statistics that would be used here One-sample t test statistics as 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 weight = 29.0 grams

            s = sample standard deviation = 0.36 grams

            n = sample of bags = 6

So, test statistics  =  [tex]\frac{29.0-28.3}{\frac{0.36}{\sqrt{6} } }[/tex]  ~ [tex]t_5[/tex]

                               =  4.763

The value of t test statistics is 4.763.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical values of -2.571 and 2.571 at 5 degree of freedom for two-tailed test.

Since our test statistics does not 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 due to which we reject our null hypothesis.

Therefore, we conclude that the true mean weight is not 28.3 grams.

There is strong evidence to suggest that the true mean weight of the Doritos bags is not 28.3 grams, based on a hypothesis test that resulted in a very low p-value.

To determine if there is strong evidence that the true mean weight of the Doritos bags is not 28.3 grams, we perform a hypothesis test using the given data.

State the null hypothesis (H0) and the alternative hypothesis (Ha):

H0: μ = 28.3 grams (the true mean weight is 28.3 grams)

Ha: μ ≠ 28.3 grams (the true mean weight is not 28.3 grams)

Calculate the test statistic:

The test statistic for a sample mean is given by:

z = (sample mean - population mean) / (standard deviation / √(n))

Here, the sample mean = 29.0 grams, population mean = 28.3 grams, standard deviation = 0.36 grams, and n = 6.

Thus, z = (29.0 - 28.3) / (0.36 / √(6)) ≈ 4.08

Using a z-table, the p-value associated with a z-score of 4.08 is extremely small (much less than 0.05).

Compare the p-value to the significance level (α):

At α = 0.05, since the p-value is much smaller, we reject the null hypothesis.

Since the p-value is very low, there is strong evidence to suggest that the true mean weight of the Doritos bags is not 28.3 grams.

Answer:

  5 miles

Step-by-step explanation:

The two legs of Deborah's hike form the right-angle legs of a right triangle. The shortest distance is then the hypotenuse of that triangle, found using the Pythagorean theorem.

  d^2 = 3^2 + 4^2 = 9 +16 = 25

  d = √25 = 5

Deborah ends 5 miles from her start.

Answer:

The probability that the​ student's IQ is at least 140 points is of 55.17%.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

University A: [tex]\mu = 150, \sigma = 77[/tex]

a) Select a student at random from university A. Find the probability that the​ student's IQ is at least 140 points.

This is 1 subtracted by the pvalue of Z when X = 140. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{140 - 150}{77}[/tex]

[tex]Z = -0.13[/tex]

[tex]Z = -0.13[/tex] has a pvalue of 0.4483.

1 - 0.4483 = 0.5517

The probability that the​ student's IQ is at least 140 points is of 55.17%.

Answer:

The expression that uses the distributive property to represent the sum of 39 + 27 is [tex]3(13 + 9)[/tex]

Step-by-step explanation:

Given

Expression: 39 + 27

Required

Express using the distributive property

The distributive property is represented in the form a(b + c)

So, we can say that the meaning to the question is that the given expression should be represented in the form a(b+c)

Equate these two expressions, we have

[tex]a(b+c) = 39 + 27[/tex]

Factorize the expression on the left hand side

[tex]a(b+c) = 3(\frac{39}{3} + \frac{27}{3})[/tex]

Simplify fraction

[tex]a(b+c) = 3(13 + 9)[/tex]

Compare expression on left hand side with the expression on the right hand side.

Since, they have the same format, then we've arrived at the answer.

Hence, the expression that uses the distributive property to represent the sum of 39 + 27 is [tex]3(13 + 9)[/tex]

The expression that represents the sum of 39 + 27 using the distributive property is 39 + 27 = (30 + 9) + (20 + 7) = 66.

The expression that represents the sum of 39 + 27 using the distributive property is:

39 + 27 = (30 + 9) + (20 + 7) = 30 + 20 + 9 + 7 = 50 + 16 = 66

To apply the distributive property, we break down the numbers into their place values and add them together. In this case, we can break down 39 into 30 + 9, and 27 into 20 + 7. Then, we add the numbers in each place value group separately and combine the results to get the final sum of 66.

https://brainly.com/question/37341329

#SPJ3

Answer:

Maricopa Success invested $55,000 in stocks

Maricopa Success invested $80,000 in bonds

Maricopa Success invested $50,000 in CDs

Step-by-step explanation:

Let S denotes stocks, B denotes bonds and C denotes CDs.

Maricopa's Success scholarship fund receives a gift of $185,000 which she invests in stocks. bonds, and CDs.

Mathematically,

S + B + C = 185,000      eq. 1

Money is invested in stocks at interest = 11.3% = 0.113

Money is invested in bonds at interest = 5.5% = 0.055

Money is invested in CDs at interest = 5% = 0.05

Annual income from the investments is $13,115

Mathematically,

0.113S + 0.055B + 0.05C = 13,115      eq. 2

Maricopa Success invests $30,000 more in bonds than in CDs.

Mathematically,

B = C + 30,000       eq. 3

Substitute the eq. 3 into eq. 1

S + B + C = 185,000

S + (C + 30,000) + C = 185,000

S + 2C + 30,000 = 185,000

S + 2C = 185,000 - 30,000

S + 2C = 155000      eq. 4

Substitute the eq. 3 into eq. 2

0.113S + 0.055B + 0.05C = 13,115

0.113S + 0.055(C + 30,000) + 0.05C = 13,115

0.113S + 0.055C + 1650 + 0.05C = 13,115

0.113S + 0.105C + 1650 = 13,115

0.113S + 0.105C = 13,115 - 1650

0.113S + 0.105C = 11,465      eq. 5

Now we have to equations and two unknowns

S + 2C = 155,000      eq. 4

0.113S + 0.105C = 11,465      eq. 5

Multiply eq. 4 by 0.113 and subract it from eq. 5

0.113S + 0.226C = 17,515

subtract it from eq. 5

0.113S + 0.105C = 11,465      eq. 5

0.113S + 0.226C = 17,515

-0.121C = -6050

0.121C = 6050

C = 6050/0.121

C = 50,000

Substitute the value of C into eq. 3

B = C + 30,000

B = 50,000 + 30,000

B = 80,000

Substitute the value of B and C into eq. 1

S + B + C = 185,000

S + 80,000 + 50,000 = 185,000

S = 185,000 - 80,000 - 50,000

S = 55,000

Therefore,

Maricopa Success invested $55,000 in stocks

Maricopa Success invested $80,000 in bonds

Maricopa Success invested $50,000 in CDs

Verification:

S + B + C = 185,000       eq. 1

55,000 + 80,000 + 50,000 = 185,000

185,000 = 185,000  (satisfied)

0.113S + 0.055B + 0.05C = 13,115      eq. 2

0.113(55,000) + 0.055(80,000) + 0.05(50,000) = 13,115

6215 + 4400 + 2500 = 13,115

13,115 = 13,115  (satisfied)

B = C + 30,000       eq. 3

80,000 = 50,000 + 30,000

80,000 = 80,000  (satisfied)

Answer:

Just divide dollar amount by unit count

2.35/24 =$ ______ per pencil

so each= =0.097917

so 97 cents

The amount that a single pencil cost is $0.10 per pencil.

Using this formula

Cost per pencil=Cost of pencil per pack/Number of pencil per pack

Where:

Cost of pencil per pack=$2.35

Number of pencil  per pack=24 pencil

Let plug in the formula

Cost per pencil=$2.35/24

Cost per pencil=$0.098

Cost per pencil=$0.10 (Approximately)

Inconclusion the amount that a single pencil cost is $0.10 per pencil.

Learn more here:

https://brainly.com/question/16698163

Answer: C. 1.942

Step-by-step explanation:

This is a test of 2 population proportions. The population proportion of the number of absent employees in plant A and plant B are p1 and p2 respectively.

From the information given,

p1 = 0.15

p2 = 0.12

n1 = 800

n2 = 1200

To determine the z score, we would first determine the pooled proportion.

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (120 + 144)/(800 + 1200) = 0.132

1 - pc = 1 - 0.132 = 0.868

The formula for z score is

z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)

z = (0.15 - 0.12)/√(0.132)(0.868)(1/800 + 1/1200) = - 0.03/0.045

z = 1.942

Using the standard error and sample difference provided in the MegaStat results, and knowing the p-value corresponds to a two-tailed test at the 5 percent significance level, the test statistic for the absenteeism rates at Melodic Kortholt Company is most likely 1.960, corresponding to Option B.

The management of Melodic Kortholt Company compared absenteeism rates in two plants on the third Monday in November. Plant A had an absenteeism rate of 120 out of 800 employees, and Plant B had a rate of 144 out of 1200 employees.

The MegaStat results provided for a two-tailed test show a sample difference of 0.03 and hypothesized difference of 0.00, with a standard error of 0.01545 and a p-value of 0.0522. To find the test statistic, we use the provided standard error and the sample difference.

Using the formula z = (sample difference - hypothesized difference) / std. error, we calculate the z-value to determine the test statistic that corresponds to the options given.

While the exact z-value isn't provided, with a p-value of 0.0522 for a two-tailed test, the z-value would be close to the critical value of 1.96 for a 95% confidence interval. Therefore, the correct z-value that matches the p-value given would most likely be Option B: 1.960.

The length of CD  to 3 significant figures is 12.7

What is the  length of CD ?

Given that;

AB=6cm AC=12cm.

Using Pythagoras in triangle ABC

[tex](AC)^{2} =(AB)^{2}+(BC)^{2}[/tex]

[tex](12)^{2} =(6)^{2}+(BC)^{2}[/tex]

[tex]144 - 36 = (BC)^{2}[/tex]

[tex](BC)^{2} =108[/tex]

[tex](BC)=\sqrt{108}[/tex]

We can then use Law of sine as;

[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

[tex]\frac{CD}{sin90} =\frac{ \sqrt{108} }{sin55}[/tex]

[tex]\frac{CD}{1} = \frac{\sqrt{50} }{sin55}[/tex]

[tex]CD=12.6866[/tex]

Answer:

c) (26.295, 28.705)

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.965}{2} = 0.0175[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.0175 = 0.9825[/tex], so [tex]z = 2.11[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.11\frac{4}{\sqrt{49}} = 1.205[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 27.5 - 1.205 = 26.295 mi/gallon

The upper end of the interval is the sample mean added to M. So it is 27.5 + 1.205 = 28.705 mi/gallon

So the correct answer is:

c) (26.295, 28.705)

It's B

Step-by-step explanation:

Start with

[tex]4x - 10 = 18[/tex]

Add 10 to both sides:

[tex]4x - 10+10 = 18+10[/tex]

This cancels the "-10" on the left hand side:

[tex]4x = 28[/tex]

Divide both sides by 4:

[tex]\dfrac{4x}{4} = \dfrac{28}{4}[/tex]

This cancels the 4 on the left hand side:

[tex]x = 7[/tex]

4x - 10 = 18| + 10

4x - 10 + 10 = 18 + 10

4x = 28| ÷ 4

4x ÷ 4 = 28 ÷ 4

x = 7

Answer:

The standard deviation of that data set is 3.8

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 55

95% of the data fall between 47.4 and 62.6. This means that 47.4 is 2 standard deviations below the mean and 62.6 is two standard deviations above the mean.

Using one of these points.

55 + 2sd = 62.6

2sd = 7.6

sd = 7.6/2

sd = 3.8

The standard deviation of that data set is 3.8

Answer:

Yes, they form a partition

Step-by-step explanation:

For a group of sets to be considered a partition of set A (currently enrolled students), all of the elements in set A must be contained in the subsets that form the partition and no individual element can be present in more than one subset.

In this situation, take set A0 for instance, all students whose ID numbers begin with 0 will be in this set and in this set alone. The same can be said for Ai  where i ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Since no other possible value can be assigned for the first digit of an student ID, it is correct to affirm that sets A0, …, A9 form a partition of the set of currently enrolled students.

Final answer:

The sets A0, A1, ..., A9, where each set consists of students whose ID starts with a specific digit, form a partition of the set of all currently enrolled students because each set is non-empty, the sets are mutually exclusive, and their union represents the entire set of students.

Explanation:

To understand if the sets A0, A1, ..., A9, form a partition of the set of currently enrolled university students based on their 8-digit ID numbers starting with digits 0 through 9, three conditions must be met: each set must be non-empty, the sets must be mutually exclusive, and their union must form the entire set of currently enrolled students.

Thus, the sets A0 through A9 form a partition of the set of all currently enrolled students.

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 152.5

For the alternative hypothesis,

µ ≠ 152.5

This is a two tailed test.

Since no population standard deviation is given, the distribution is a student's t.

Since n = 231

Degrees of freedom, df = n - 1 = 231 - 1 = 230

t = (x - µ)/(s/√n)

Where

x = sample mean = 148.9

µ = population mean = 152.5

s = samples standard deviation = 27.4

t = (148.9 - 152.5)/(27.4/√231) = - 2

We would determine the p value using the t test calculator. It becomes

p = 0.047

Since alpha, 0.05 > thanthere sufficient evidence to conclude that the self-efficacy of adults who have experienced childhood trauma differs from that in the general population of individuals the p value, 0.047, then we would reject the null hypothesis. Therefore, At a 5% level of significance, there is sufficient evidence to conclude that the self-efficacy of adults who have experienced childhood trauma differs from that in the general population of individuals

Answer:

I think the answer is 292 inches.

Answer: 250in².

Step-by-step explanation:

Total surface area of the fish tank wil be, listen we can can derive a formula for the surface area.

The fish tanks has five surfaces since the top will be opened. For fnd the total surface area now, find the area of each of the surfaces and add together. If it is 6 surfaces, the formula would have been.

2(lb) + 2(lb) + 2(lb)

2( lb + lb + lb )

Now , first (lb) = 7 × 6in²= 42in² ie. the top and the bottom,

Second surfaces, the sides

7 × 8 = 56in²

The third is the other sides

6 × 8 = 48in². Now applying the formula now, bearing in mind that the top is open, we now have

42in² + 2( lb + lb )in²

= 42 + 2( 56 + 48 )

= 42 + 2(104)

= 42 + 208

= 250in².

Note, if the tank or box is closed, then the above derived formula could be suitable.

The height is also regarded as the depth.

Answer:

-1/2

Step-by-step explanation:

Point L is at (-2,3)

Point M is at (2,1)

We can find the slope using

m =(y2-y1)/(x2-x1)

   = (1-3)/(2 - -2)

    =(1-3)/(2+2)

   =-2/4

  =-1/2

Answer:

Step-by-step explanation:

Given that,

The reference angle is 35°

It lies in the fourth quadrant.

The reference angle is the positive acute angle that can represent an angle of any measure.

The reference angle  must be < 90∘.

In radian measure, the reference angle  must be < π/ 2.

Basically, any angle on the x-y plane has a reference angle, which is always between 0 and 90 degrees. The reference angle is always the smallest angle that you can make from the terminal side of an angle (ie where the angle ends) with the x-axis. A reference angle always uses the x-axis as its frame of reference.

Since the reference angle is less than 35°, then, the reference angle is positive,

The negative angle is 360 - 35 = 325°

So, the positive reference angle is 35° and the negative reference angle is 325°

This question is based on concept of reference angle.Therefore, the positive measures for the angle would be 35° and the negative would be 325°.

Given:

The reference angle is 35º and its terminal side lies in [tex]\bold{4^{th}}[/tex] Quadrant .

By the definition of reference angle,

An angle's reference angle is the measure of the smallest, positive, acute angle formed by the terminal side of the angle and the horizontal axis.

Thus, positive reference angles have terminal sides that lie in the first quadrant and can be used as models for angles in other quadrants.

The reference angle is acute angle.Therefore, it must be < 90°.

In radian measure, it must be less than  [tex]\bold{\dfrac{\pi }{2}}[/tex].

Therefore, the reference angle is less than 35°. So, reference angle is positive.And the negative angle is 360 - 35 = 325°.

Therefore, the positive measures for the angle would be 35° and the negative would be 325°.

For further details, please refer this link:

https://brainly.com/question/1061317