Plz I need help with this question

Plz I Need Help With This Question

Answers

Answer 1

Answer:

adjacentobtuse

Step-by-step explanation:

The angles marked 1 and 2 share the vertical line as a common side, so they are "adjacent" angles. Each is the sum of an acute angle and a right angle, so is "obtuse."

None of the other descriptors apply.


Related Questions

A square with side lengths of 3 cm is reflected vertically over a horizontal line of reflection that is 2 cm below the bottom edge of the square. What is the distance between the points C and C’? cm What is the perpendicular distance between the point B and the line of reflection? cm What is the distance between the points A and A’? cm

Answers

Answer:

a) 4 cm

b) 5 cm

c) 10 cm

Step-by-step explanation:

The side lengths of the reflected square are equal to the original, and the distance from the axis(2) also remains the same.  From there, it is just addition.

Hope it helps <3

Answer:

A) 4

B) 5

C) 10

Step-by-step explanation:

edge2020

A consultant wants to ask workers at a factory about the workers' job satisfaction. Which of the following best describes a cluster sample of workers?

a. The consultant takes a list of the workers and selects every 6" worker until 60 workers are selected.
b. The consultant forms 5 groups of workers based on the workers' shifts. Then, he selects 12 workers at random from each group.
c. The consultant forms groups of 12 workers based on the lengths of time the workers have worked at the factory. Then, he randomly chooses 5 groups and selects all of the workers in these groups

Answers

Answer:

i think option c must be correct because it has formed the grops on the basis of length of time and made the group by random selection.

A new fertilizer was applied to the soil of 146 bean plants. 23% showed increased growth. Find the margin of error and 95% confidence interval for the percentage of all bean plants which show increased growth after application of the fertilizer. Round all answers to 2 decimal places.

Answers

Answer:

The significance level for this case would be [tex]\alpha=1-0.95=0.05[/tex] and the critical value for this case would be:

[tex] z_{\alpha/2}=1.96[/tex]

The margin of error is given by:

[tex] ME = z_{\alpha/2} \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

And replacing we got:

[tex] ME = 1.96 \sqrt{\frac{0.23*(1-0.23)}{146}} =0.0683[/tex]

And the margin of error for this case would be [tex] ME = 0.07[/tex]

Step-by-step explanation:

For this case we have the following dataset given:

[tex] n= 146[/tex] represent the sample size

[tex] \hat p =0.23[/tex] represent the estimated proportion of interest

[tex] Conf=0.95[/tex] represent the confidence level

The significance level for this case would be [tex]\alpha=1-0.95=0.05[/tex] and the critical value for this case would be:

[tex] z_{\alpha/2}=1.96[/tex]

The margin of error is given by:

[tex] ME = z_{\alpha/2} \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

And replacing we got:

[tex] ME = 1.96 \sqrt{\frac{0.23*(1-0.23)}{146}} =0.0683[/tex]

And the margin of error for this case would be [tex] ME = 0.07[/tex]

Pls help me help me​

Answers

Answer:

C.

Step-by-step explanation:

When two lines are parallel, their slopes are the same.

Since the slope of line l is 2/7, the slope of its parallel line m must also be 2/7.

The answer is C.

Answer:

C. 2/7

Step-by-step explanation:

Parallel lines are lines that have the same slopes.

We know that line l is parallel to line m.

Therefore, the slope of line l is equal to the slope of line m.

[tex]m_{l} =m_{m}[/tex]

We know that line l has a slope of 2/7.

[tex]\frac{2}{7} =m_{m}[/tex]

So, line m also has a slope of 2/7. The answer is C. 2/7

What is the distance between (−11, −20) and (−11, 5)?

−25 units

−15 units

15 units

25 units

Answers

-15 units
Because -11 and -20 has a difference if -9 and -11 and 5 has a difference of 6 but it’s asking for difference so it’s -6 and when those are combined it’s -15.

Answer:

IT'S NOT -15 FOR SUREEE

Step-by-step explanation:

I Believe it's 15

The surface area of an open-top box with length L, width W, and height H can be found using the
formula:
A = 2LH + 2WH + LW
Find the surface area of an open-top box with length 9 cm, width 6 cm, and height 4 cm.

Answers

Answer:

174 square cm

Step-by-step explanation:

2(9×4) + 2(6×4)+ 9×6

2(36) + 2(24) + 54

72 + 48 + 54

120 + 54

174

: Bobby's Burger Palace had its
grand opening on Tuesday,
They had 164 1/2 lb of ground
beef in stock. They had 18 1/4
Ib left at the end of the day.
Each burger requires 1/4 lb of
ground beef. How many
hamburgers did they sell?

Answers

Answer: 585 burgers

Explanation:
164 1/2 = 329/2
18 1/4 = 73/4

Find the amount used:
329/2 - 73/4
= 658/4 - 73/4
= 585/4

Find the amount of burger made:

585/4 divide by 1/4
= 585/4 x 4/1
= 585

A respiratory therapist predicts that the proportion of U.S. college students who smoke hookah is greater than 30%. To test this prediction, she surveys 300 random U.S. college, and it is determined that 80 of them smoke hookah. The following is the setup for this hypothesis test: H0:p=0.30 H0:p>0.30 The p-value for this hypothesis test is 0.10. At the 5% significance level, should she reject or fail to reject the null hypothesis? Select the correct answer below: Reject the null hypothesis because 0.30>0.05. Fail to reject the null hypothesis because 0.30>0.05. Reject the null hypothesis because the p-value =0.10 is less than the significance level α=0.05. Fail to reject the null hypothesis because the p-value =0.10 is more than the significance level α=0.05.

Answers

Answer:

Fail to reject the null hypothesis because the p-value =0.10 is more than the significance level α=0.05.

Step-by-step explanation:

The significant level for this case study is 5% - 0.05. If the results gotten is less than the significance level, we reject the null hypothesis, but if greater, we fail to reject the null hypothesis.

In this case study, the p-value is 0.10 which is a lot higher than 0.05, thus we will fail to reject the null hypothesis because the p-value =0.10 is more than the significance level α=0.05.

If Brooklyn College students have an IQ of 100, on average, with a standard deviation of 16 points, and I collect 48 BC Psychology students to see how Psych majors compare to all of BC, find the following:_______.
1. mu =
2. sigma =
3. mu _x bar =
4. sigma _x bar =

Answers

Answer:

1  [tex]\mu = 100[/tex]

2 [tex]\sigma = 16[/tex]

3 [tex]\mu_x = 100[/tex]

4 [tex]\sigma _{\= x } = 2.309[/tex]

Step-by-step explanation:

From the question

    The population mean is  [tex]\mu = 100[/tex]

    The standard deviation is [tex]\sigma = 16[/tex]

     The sample mean is  [tex]\mu_x = 100[/tex]

     The sample size is  [tex]n = 48[/tex]

     The mean standard deviation is  [tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

     [tex]\sigma _{\= x } = \frac{16 }{\sqrt{48} }[/tex]

     [tex]\sigma _{\= x } = 2.309[/tex]

A random sample has been taken from a normal distribution and the following confidence intervals constructed using the same data: (25.53, 37.87) and (23.59, 39.81). One of these intervals is a 99% CI and the other is a 95% CI. Please match them.

Answers

Answer:

(25.53, 37.87): 95% CI

(23.59, 39.81): 99% CI

Step-by-step explanation:

The margin of error of a confidence interval is given by:

[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.

z is related to the confidence level. The higher the confidence level, the higher the values of z, and thus, we wider the confidence interval is.

In this question:

The narrower C.I. is the 95%, and the wider is the 99%. So

(25.53, 37.87): 95% CI

(23.59, 39.81): 99% CI

Consider a cupcake shop that sells 7 different kinds of cupcakes (chocolate raspberry, strawberry shortcake, red velvet, funfetti, lemon, German chocolate, and chocolate caramel). Assuming there are at least 12 of each kind available, if Andres asks for a random selection of 12 cupcakes, what is the probability that he will get
(a)exactly 6 red velvet?
(b)exactly 3 each of 4 different kinds?
(c)no lemon?
(d)at least 1 German chocolate and at least one chocolate raspberry?

Answers

Answer:

If Andres asks for a random selection of 12 cupcakes, the Probability of choosing:

a)exactly 6 red velvet?

The probability that 6 will be red velvet = 6/12 x 14.3% = 7.2%

(b)exactly 3 each of 4 different kinds?

Since 3 x 4 = 12

The probability that the 12 will be 3 each from 4 different kinds

= 14.3%

(c)no lemon?

Probability of getting a lemon cupcake = 1/7 = 14.3%

Therefore, probability of not getting a lemon cupcake = 100% - 14.3% = 85.7%

(d)at least 1 German chocolate and at least one chocolate raspberry?

The probability of at least 2 being 1 German and 1 chocolate raspberry

= 2/12

= 16.67%

Step-by-step explanation:

a) Probability of each kind of Cupcake

Kind of Cupcakes         Quantity  Probability

chocolate raspberry      12            14.285%

strawberry shortcake    12            14.3%    

red velvet                       12            14.3%

funfetti                            12            14.3%

lemon                             12            14.3%

German chocolate         12            14.3%

chocolate caramel         12            14.3%

b) The probability of choosing a kind of cupcake is the chance that, for example, a strawberry cupcake is chosen instead of the other six kinds.  It expresses the opportunity that an event has in happening out of many other events that could have happened.

The given equation has been solved in the table.

Answers

Answer:  D. Subtraction property not used

The closest we get is the addition property, which was used in step 2. This is a fairly similar idea because subtraction is effectively adding on a negative number. Example: 5-7 = 5+(-7). Though because your teacher is making a distinction between addition property of equality and subtraction property of equality, it's safe to say that the subtraction property is not used.

Vance ate a salad and Four-fifths of a turkey burger for dinner. The salad contained 80 calories and his entire meal contained 440 calories. Which equation can be used to determine x, the number of calories in the entire turkey burger?

Answers

The correct answer is A. 440 = [tex]\frac{4}{5}[/tex] x + 80

Explanation:

In mathematics, equations are often used to find an unknown value. Additionally, equations display two mathematical expressions that have an equality relation, and based on this equality the unknown value can be found. Moreover, if you need to write an equation it is important to include all the important values, and understand the relationship between them because this determines the mathematical signs that need to be used.

In the case presented, it is known the total of the calories for the burger and salad is 440. Because of this, the mathematical expression on one side should be 440. Additionally, on the other side, it is necessary to include the calories of the salad (80) plus the calories of the burger. However, because you know Vance ate only 4/5 of the burger and the value of the burger is not known the correct expression for this section is [tex]\frac{4}{5}[/tex] x as x represents the unknown value. Thus, the correct equation is "440 = [tex]\frac{4}{5}[/tex] x + 80"

Answer:

The correct answer is A. 440 = 4/5x + 80

WHAT IS THE ANSWER ?? PLEASE HELP !!

Answers

Answer:

B. 43°

Step-by-step explanation:

Internal angles of the triangle are:

180°-90°=90° and180°-133°= 47°

So It is a right triangle and the missing angle is:

p= 90°- 47°= 43°

Answer:

The answer is B) 43°

Step-by-step explanation:

180° - 133° = 47° (that's one of the angles inside the triangle)

180° - 90° = 90° (the other angle)

Every angle inside a triangle added equals 180°, therefor:

180° - (47° + 90°) = 43°

Find the value of s(t(-2)):
s(x)= - 3x-2
t(x)=5x-4

Answers

Answer: s(t(-2)) is 40
Explanation: first let’s find figure out t(-2) first before we move on to the next one

t(x) = 5x-4
t(-2)= 5(-2)-4= -14

Now that we know t(-2) = -14
Then let’s find s(x) where x is -14

s(x)= -3x-2
s(-14)= -3(-14)-2= 42-2=40

And s(t(-2)) = 40

Identify the slope and y-intercept of the line −2x+5y=−30.

Answers

Answer:

slope = 2/5   ,    y-intercept = -30

Step-by-step explanation:

-2x + 5y = -30

5y  = 2x - 30

y = 2/5x - 6

we know that the general form is:

y = (slope)*x + (y- intercept)

so, from our equation, we can say that...

slope = 2/5

y- intercept = -30

Find A x B, where A=(5i+j) , B=(i-5j)

Answers

Answer:

5i² - 25ij +ji-5j²

Step-by-step explanation:

Use distributive property

Answer:

The answer is 5i² - 24ij - 5j²

Step-by-step explanation:

A = (5i+j)

B = (i-5j)

A × B is

( 5i + j) ( i - 5j)

Expand

We have

5i² - 25ij + ij - 5j²

The final answer is

5i² - 24ij - 5j²

Hope this helps you.

The dose of a drug is 0.05 mg for each kg of a patient’s weight.The Drug is available as an oral liquid containing 50 mcg/0.1 ml.Calculate the dose of the oral liquid in ml for a patient who weighs 132 lb

Answers

Answer:

  6 mL

Step-by-step explanation:

It is a matter of units conversion.

  volume = (mass) × (dose/mass) ÷ (dose/volume)

  (132 lb)/(2.2 kg/lb) × (0.05 mg/kg) / (0.05 mg/0.1 mL) = 6 mL

Peter samples her class by selecting 5 girls and 7 boys. This type of sampling is called?​

Answers

Answer:

Hello!

______________________

Peter samples her class by selecting 5 girls and 7 boys. This type of sampling is called?​

This type of sampling is called Stratified.

Hope this helped you!

:D

P-value test and Ctitical Value test are identical. P-value and Critical value are two different names for the same steps. They can be used interchangeably.
a. true
b. false

Answers

Answer:

Option B - False

Step-by-step explanation:

Critical value is a point beyond which we normally reject the null hypothesis. Whereas, P-value is defined as the probability to the right of respective statistic which could either be Z, T or chi. Now, the benefit of using p-value is that it calculates a probability estimate which we will be able to test at any level of significance by comparing the probability directly with the significance level.

For example, let's assume that the Z-value for a particular experiment is 1.67, which will be greater than the critical value at 5% which will be 1.64. Thus, if we want to check for a different significance level of 1%, we will need to calculate a new critical value.

Whereas, if we calculate the p-value for say 1.67, it will give a value of about 0.047. This p-value can be used to reject the hypothesis at 5% significance level since 0.047 < 0.05. But with a significance level of 1%, the hypothesis can be accepted since 0.047 > 0.01.

Thus, it's clear critical values are different from P-values and they can't be used interchangeably.

the bus fare in a city is $2.00. people who use the bus have the option of purchashing a monthly coupoun book is $20.00. with the copoun bok, the fare is reduced to $1.00 Determine the number of times in a month the bus be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book

Answers

Answer:

but I can do it if you want but I don't you too too y u your help and you have time can you

Step-by-step explanation:

guy who was it that you are not going to be able to make it to the meeting tonight but I can tomorrow if you have time can you come to my house

An efficiency expert hired by a manufacturing firm has compiled these data relating workers output to their experience:
Experience t (months) 0 3
Output Q (units per hour) 200 190
Suppose output Q Is related to experience t by a function of the form Q (t) = 300 - A e^-kt. Find the function of this form that fits the data.

Answers

Answer:

Q(t) = 300 - 100e^0.0318t

Step-by-step explanation:

Given the relationship between the output as related to the experience t to be Q (t) = 300 - A e^-kt.

From the table, at t = 0, Q(t) = 200, substituting this into he equation to get A we have:

200 = 300 - A e^-k(0).

200 = 300 - A e^-0

200 = 300 - A

A = 300-200

A = 100

Secondly we need to get the constant k by substituting the other condition into the equation. When t = 3, Q(t) = 190

190 = 300 - A e^-k(3)

190 = 300 - 100e^-3k

190-300 = -100e^-3k

-110 = -100e^-3k

e^-3k = -110/-100

e^-3k = 1.1

Taking the natural logarithm of both sides we have;

ln(e^-3k) = ln1.1

-3k = 0.09531

k = 0.09531/-3

k = -0.0318

The function of this form that fits the data can be gotten by substituting A = 100 and k = -0.0318 into the modeled equation given as shown:

Q(t) = 300 - A e^-kt

Q(t) = 300 - 100e^-(-0.0318)t

Q(t) = 300 - 100e^0.0318t

Bread recipe calls for 2 1/2 cups of whole wheat flour 2/3 cup of rice flour 2 1/4 cups of white flour how many total cups of flour are needed write your answer as a simplified mixed number

Answers

Answer:

5 5/12

Step-by-step explanation:

u first find the common denominator which is 12

2 6/12

8/12

2 3/12

now u add them all

hope this helps

A statistics tutor wants to assess whether her remedial tutoring has been effective for her five students. She decides to conduct a related samples t-test and records the following grades for students prior to and after receiving her tutoring.
Tutoring
Before After
2.4 3.1
2.5 2.8
3.0 3.6
2.9 3.2
2.7 3.5
Test whether or not her tutoring is effective at a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.)
t =
Compute effect size using estimated Cohen's d. (Round your answer to two decimal places.)
d =

Answers

Answer:

The test statistic value is, t = -5.245.

The effect size using estimated Cohen's d is 2.35.

Step-by-step explanation:

A paired t-test would be used to determine whether the remedial tutoring has been effective for the statistics tutor's five students.

The hypothesis can be defined as follows:

H₀: The remedial tutoring has not been effective, i.e. d = 0.

Hₐ: The remedial tutoring has been effective, i.e. d > 0.

Use Excel to perform the Paired t test.

Go to Data → Data Analysis → t-test: Paired Two Sample Means

A dialog box will open.

Select the values of the variables accordingly.

The Excel output is attached below.

The test statistic value is, t = -5.245.

Compute the effect size using estimated Cohen's d as follows:

[tex]\text{Cohen's d}=\frac{Mean_{d}}{SD_{d}}[/tex]

                [tex]=\frac{0.54}{0.23022}\\\\=2.34558\\\\\approx 2.35[/tex]

Thus, the effect size using estimated Cohen's d is 2.35.

Suppose that a certain brand of light bulb has a mean life of 450 hours and a standard deviation of 73 hours. Assuming the data are bell-shaped: (Show work to get full credit)
a. Would it be unusual for a light bulb to have a life span of 320 hours? 615 hours? Justify each response.
b. According to the Empirical Rule, 99.7% of the light bulbs have a lifetime between what two values?
c. Determine the percentage of light bulbs that will have a life between 304 and 596 hours.

Answers

Answer:

yes it is correct

Step-by-step explanation:

plz give brainliest.

Ben bought the enormous box of juice shown below. He drinks 450 cubic centimeters of juice each day. How many days does it take Ben to drink the box of juice?

Answers

Answer:

Step-by-step explanation:

to find the answer you have to find the vulume and then divide by 450

Answer:

7 days

Step-by-step explanation:

vol = 20*15*10.5

vol = 3150

how many days  to drink 3150 cu.cm if Ben drinks 450 cu.cm per day?

3150 cu.cm / 450 cu.cm per day = 7 days

An object of mass 2kg is attached to a spring. A force of 5nt is applied to move the object 0.5m from its equilibrium position. The damping force of the object sliding on the table is int when the velocity is 0.25m/second. The object is pulled to the left until the spring is stretched lm and then released with the initial velocity of 2m/second to the right.
Set up an I.V.P. to describe the motion of the object and solve it, then state the amplitude function of the motion.

Answers

Answer:

[tex]\mathbf{x(t) = \dfrac{ \sqrt 5}{2}e^{-t} }[/tex]

Step-by-step explanation:

Given that:

mass of the object = 2 kg

A force of 5nt is applied to move the object 0.5m from its equilibrium position.

i.e

Force = 5 newton

Stretchin (x) =0.5 m

Damping force = 1 newton

Velocity = 0.25 m/second

The object is pulled to the left until the spring is stretched lm and then released with the initial velocity of 2m/second to the right

SOLUTION:

If F = kx

Then :

5 N = k(0.5 m)

where ;

k = spring constant.

k = 5 N/0.5 m

k = 10 N/m

the damping force of the object sliding on the table is 1 newton when the velocity is 0.25m/second.

SO;

[tex]C \dfrac{dx}{dt}= F_d[/tex]

[tex]C* 0.25 = 1[/tex]

C = [tex]\dfrac{1 \ N }{0.25 \ m/s}[/tex]

C = 4 Ns/m

NOW;

[tex]m \dfrac{d^2x}{dt^2}+ C \dfrac{dx}{dt}+ kx = 0[/tex]

Divide through by m; we have;

[tex]\dfrac{m}{m}\dfrac{d^2x}{dt^2}+ \dfrac{C}{m} \dfrac{dx}{dt}+ \dfrac{k}{m} x= 0[/tex]

[tex]\dfrac{d^2x}{dt^2}+ \dfrac{C}{m} \dfrac{dx}{dt}+\dfrac{k}{m}x= 0[/tex]

[tex]\dfrac{d^2x}{dt^2}+ \dfrac{4}{2} \dfrac{dx}{dt}+\dfrac{10}{2}x= 0[/tex]

[tex]\dfrac{d^2x}{dt^2}+ 2 \dfrac{dx}{dt}+5x= 0[/tex]

we all know that:

[tex]x(t) = Ae^{(\alpha \ t)}[/tex]  ------ (1)

SO;

[tex]\alpha ^2 + 2\alpha + 5 = 0[/tex]

[tex]\alpha = \dfrac{-2 \pm \sqrt{(4)-(4*5)}}{2}[/tex]

[tex]\alpha = -1 \pm 2i[/tex]

Thus ;

[tex]x(t) = e^{-t}[A \sin (2t)+ B cos (2t)][/tex]   ------------ (1)

However;

[tex]\dfrac{dx}{dt} = e^{-t}[A \sin (2t)+ B cos (2t)]+ 2e ^{-t} [A \cos (2t)- B \ Sin (2t)][/tex]     ------- (2)

From the question ; we are being told that;

The object is pulled to the left until the spring is stretched 1 m and then released with the initial velocity of 2m/second to the right.

So ;

[tex]x(0) = -1 \ m[/tex]

[tex]\dfrac{dx}{dt}|_{t=0} = 2 \ m/s[/tex]

x(0) ⇒ B = -1

[tex]\dfrac{dx}{dt}|_{t=0} =- B +2A[/tex]

[tex]=- 1 +2A[/tex]

1 = 2A

A = [tex]\dfrac{1}{2}[/tex]

From (1)

[tex]x(t) = e^{-t}[A \sin (2t)+ B cos (2t)][/tex]  

[tex]x(t) = e^{-t}[\dfrac{1}{2} \sin (2t)+ (-1) cos (2t)][/tex]

[tex]x(t) = e^{-t}[\dfrac{1}{2} \sin (2t)-cos (2t)][/tex]

Assuming;

[tex]A cos \ \phi = \dfrac{1}{2}[/tex]

[tex]A sin \ \phi = 1[/tex]

Therefore:

[tex]A = \sqrt{\dfrac{1}{4}+1}[/tex]

[tex]A = \sqrt{\dfrac{1+4}{4}}[/tex]

[tex]A = \sqrt{\dfrac{5}{4}}[/tex]

[tex]A ={ \dfrac{ \sqrt5}{ \sqrt4}}[/tex]

[tex]A ={ \dfrac{ \sqrt5}{ 2}}[/tex]

where;

[tex]\phi = tan ^{-1} (2)[/tex]

Therefore;

[tex]x(t) = \dfrac{\sqrt 5}{2}e^{-t} \ sin (2 t - \phi)[/tex]

From above ; the amplitude is ;

[tex]\mathbf{x(t) = \dfrac{ \sqrt 5}{2}e^{-t} }[/tex]

Construct 3 linear equation starting with qiven solution z = 1/3

Answers

Answer:

(a)[tex]9z+2=5[/tex]

(b)[tex]21z-11=-4[/tex]

(c)[tex]4z=2-2z[/tex]

Step-by-step explanation:

We are required to construct 3 linear equations starting with the given solution z = 1/3.

Equation 1

[tex]z=\frac{1}{3}[/tex]

Multiply both sides by 9

[tex]9z=\frac{1}{3}\times 9\\9z=3[/tex]

Rewrite 3 as 5-2

9z=5-2

Add 2 to both sides

Our first equation is: [tex]9z+2=5[/tex]

Equation 2

[tex]z=\frac{1}{3}[/tex]

Multiply both sides by 21

[tex]21z=\frac{1}{3}\times 21\\21z=7[/tex]

Rewrite 7 as 11-4

21z=11-4

Subtract 11 from both sides

Our second equation is: [tex]21z-11=-4[/tex]

Equation 3

[tex]z=\frac{1}{3}[/tex]

Multiply both sides by 6

[tex]6z=\frac{1}{3}\times 6\\6z=2[/tex]

Rewrite 6z as 4z+2z

4z+2z=2

Subtract 2z from both sides

Our third equation is: [tex]4z=2-2z[/tex]

A(2,9), B(4,k), and C(9, -12) are 3 collinear points.
Find the value of k.

Answers

Answer is   3

==========================================================

Explanation:

We're going to be using the slope formula a bunch of times.

Find the slope of the line through points A and C

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

m = (-12-9)/(9-2)

m = -21/7

m = -3

The slope of line AC is -3. The slopes of line AB and line BC must also be the same for points A,B,C to be collinear. The term collinear means all three points fall on the same straight line.

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Let's find the expression for the slope of line AB in terms of k

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

m = (k-9)/(4-2)

m = (k-9)/2

Set this equal to the desired slope -3 and solve for k

(k-9)/2 = -3

k-9 = 2*(-3) ..... multiply both sides by 2

k-9 = -6

k = -6+9 .... add 9 to both sides

k = 3

If k = 3, then B(4,k) updates to B(4,3)

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Let's find the slope of the line through A(2,9) and B(4,3)

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

m = (3-9)/(4-2)

m = -6/2

m = -3 we get the proper slope value

Finally let's check to see if line BC also has slope -3

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

m = (-12-3)/(9-4)

m = -15/5

m = -3 we get the same value as well

Since we have found lines AB, BC and AC all have slope -3, we have proven that A,B,C fall on the same straight line. Therefore, this shows A,B,C are collinear.

A school is 16km due west of a school q.
What is the bearing of q from p?


Answers

Answer:

16 km due west

Step-by-step explanation:

The bearing of the school p from school q is 16 km due west.

To find the bearing of school q from school p, we have to find the direction that the school q is with respect to school p.

Since p is directly west of q, then it implies that q must be directly east of p.

We now know the direction.

Since the distance from q to p is exactly the same as the distance from p to q, then, the distance from p to q is 16 km.

Hence, the bearing of q from p is 16 km due west.

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