4. What kind of triangle is made by connecting the points A(0, –6), B(3, –6), and C(3, –2)?
equilateral
right
isosceles
right and isosceles
5. What type of quadrilateral is formed by connecting the points (0, 9), (3, 6), (0, 1), and (–3, 6)?
rhombus
trapezoid
kite
quadrilateral ...?

1. The vertices B, D and R have coordinates (9,9), (1,5) and (11,5), respectively. Then

[tex] BR=\sqrt{(11-9)^2+(5-9)^2}=\sqrt{4+16} = 2\sqrt{5} ,\\BD=\sqrt{(1-9)^2+(5-9)^2}=\sqrt{64+16} = 4\sqrt{5}. [/tex]

The ratio

[tex] \dfrac{BR}{BD}= \dfrac{2\sqrt{5}}{4\sqrt{5}} =\dfrac{1}{2}. [/tex]

2. The vertices K, E and Y have coordinates (13,9), (14,10) and (14,2), respectively. Then

[tex] KE=\sqrt{(13-14)^2+(9-10)^2}=\sqrt{1+1} = \sqrt{2} ,\\KY=\sqrt{(13-14)^2+(9-2)^2}=\sqrt{1+49} = 5\sqrt{2}. [/tex]

The ratio

[tex] \dfrac{KE}{KY}= \dfrac{\sqrt{2}}{5\sqrt{2}} =\dfrac{1}{5}. [/tex]

Answer: correct answer is C (they are not similar because segment BR to segment DB is 1:2 and segment KE to segment YK is 1:5.)

The difference between 90 pence and 3 pounds 25 pence is 235 pence, or 2 pounds 35 pence.

The question is asking for the difference between two amounts of money, 90 pence (90p) and 3 pounds 25 pence (£3.25). To find the difference, you would subtract the smaller amount from the larger amount. In this scenario, since both amounts are in British currency, it is a straightforward subtraction.

£3.25 is equal to 325 pence (since there are 100 pence in a pound). Now, subtract:

325p - 90p = 235p

Therefore, the difference between 90p and £3.25 is 235 pence, which can also be expressed as £2.35.

Answer:

(a) Number the residents using the latest census data, then use a random number generator to pick 48 people.

(b) The 1744 listeners who logged in and indicated their preference

Step-by-step explanation:

(a) Sampling method is said to be Simple Random Sampling if unit from the population are drawn randomly without any criteria, such that each unit as same chance of selection.

Since, In only first option each unit has same chance of selection. Thus, method of selection is  Simple Random Sample.

(b) Since, population of interest is asked and 1744 listeners logged on in the support of State Park.

Thus, first option is correct.

we have

[tex]f(x)=\sqrt{x}+12[/tex]

[tex]g(x)=2\sqrt{x}[/tex]

we know that

[tex](f-g)(144)=f(144)-g(144)[/tex] -------> equation A

Step 1

Find the value of [tex]f(144)[/tex]

For [tex]x=144[/tex]

substitute in f(x)

[tex]f(144)=\sqrt{144}+12[/tex]

[tex]f(144)=12+12[/tex]

[tex]f(144)=24[/tex]

Step 2

Find the value of [tex]g(144)[/tex]

For [tex]x=144[/tex]

substitute in g(x)

[tex]g(144)=2\sqrt{144}[/tex]

[tex]g(144)=2(12)[/tex]

[tex]g(144)=24[/tex]

Step 3

Find [tex](f-g)(144)[/tex]

Substitute the values in the equation A

[tex]24-24=0[/tex]

therefore

the answer is the option

[tex]0[/tex]

When cos2X=1/3 and 0<=2X<=pi, you can use the double angle formula for cosine to solve for cosX. The result is sqrt(6)/3.

To solve for cosX given that cos2X=1/3 and 0<=2X<=pi, you need to use the double angle formula for cosine, which is:

cos2X = 2cos²X - 1

Plugging in 1/3 for cos2X, we get:

1/3 = 2cos²X - 1

Solving this equation for cos²X gives us :

cos²X = 2/3

The square root of this is ±sqrt(2/3), or ±sqrt(2)/sqrt(3). However, since X falls in the range 0<=X<=pi/2 (because 0<=2X<=pi), cosX is positive. Therefore:

cosX = sqrt(2)/sqrt(3) = sqrt(6)/3

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Answer: For Plato users

A. The closing costs are $16,500 ,and the down payment is $41,250

Step-by-step explanation:

Just took the test

The closing costs are $16,500, & the down payment is $41,250.Option A is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol. The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages.

It is given that, Steve is buying a home worth $275000. His closing costs will amount to 6%, & his down payment is 15%

Closing cost = 6 % of $275000

Closing cost = 6/100 × $275000

Closing cost = $16500

Down payment = 15% of  $275000

Down payment = 15/100 × $275000

Down payment =  $41,250.

Thus closing costs are $16,500, & the down payment is $41,250.Option A is correct.

Learn more about the percentage here:

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Answer: Hi!

in a probability table, the x represents a given event, and p is the probability of such event.

There are two rules if you have n events; then p₁ + p₂ + ... + pₙ = 1, this is because the probability is normalized.

whit this info you can discard the third option, because there is a probability bigger than 1, and then the addition of al the probabilities is bigger than 1.

The second rule is that there do not exist negative probabilities (because they don't have sense) then you can also discard the second option.

Now we need to check the first and the fourth options, we need to add the 4 probabilites in each and see if the result is 1.

for the first options we have :  

0.2 + 0.35 + 0.15 + 0.25 = 0.95

this is not normalized, this is not a probability distribution table.

for the fourth option we have:

0.4 + 0.15 + 0.25 + 0.2 = 1

this is normalized, then this is a probability distribution table.

Then the only right answer is option 4.

Answer:

the answer is  (,2)

Step-by-step explanation:

the system of solutions is the point that two equations/line cross

the two lines cross at (1,2)

Answer:

72

Step-by-step explanation:

Answer: 4 days and 18 hours

Step-by-step explanation:

Answer: C)  {0 ≤ h ≤ 25}

Step-by-step explanation:

Given: The amount earned by Hailey for one hour work =$9.50

She determines that her salary is modeled by the function [tex]s = 9.5h[/tex].

Here h is the independent variable such that 's' is dependent on 'h'.

Since she never works more than 25 hours in a week.

Therefore, the maximum hours she will work = 25

Hence, the domain of this function in this situation is {0 ≤ h ≤ 25}, where h is number of hours she works.

Answer:

[tex]12x^8-3x^9+6x^4[/tex]

B is the correct option.

Step-by-step explanation:

We have to multiply the expression

[tex]3x^4(4x^4-x^5+2)

Using the distributive property a(b+c)=ab+ac

[tex]3x^4\times4x^4+3x^4\times(-x^5)+3x^4\times2[/tex]

Now, using the exponent rule [tex]x^a\times x^b=x^{a+b}[/tex]

[tex]12x^{4+4}-3x^{4+5}+6x^4[/tex]

On simplifying, we get

[tex]12x^8-3x^9+6x^4[/tex]

B is the correct option.

The values of x at which f(x) = x^4 - 18x^2 has a critical point and changes from decreasing to increasing are x = 3 and x = -3.

To determine at what values of x the function f(x) = x^4 - 18x^2 has critical points where the graph changes from decreasing to increasing, we must find the first derivative of f(x), set it to zero, and solve for x. The first derivative of f(x) is f'(x) = 4x^3 - 36x. Setting the derivative to zero gives us 4x^3 - 36x = 0, which can be factored as 4x(x^2 - 9) = 0. The solutions to this are x = 0, x = 3, and x = -3.

Next, to determine if these points are minima (where the graph changes from decreasing to increasing), we must examine the second derivative, or use the first derivative test. The second derivative f''(x) is 12x^2 - 36. Entering our critical points into this equation, we find that for x = ±3, the second derivative is positive, indicating a minima, whereas for x = 0, the second derivative is negative, which indicates a maxima.

Thus, the values of x at which f(x) has a critical point and the graph changes from decreasing to increasing are at x = 3 and x = -3.

The critical points of the function [tex]f(x) = x^4 - 18x^2[/tex], we need to find the derivative f'(x) and set it equal to zero. The critical points are x = 0, -3, and 3. At x = -3, the graph changes from decreasing to increasing.

The critical points of the function[tex]f(x) = x^4 - 18x^2,[/tex] we need to find the derivative f'(x) and set it equal to zero. Let's find the derivative:

[tex]f(x) = x^4 - 18x^2[/tex]

[tex]f'(x) = 4x^3 - 36x[/tex]

Now, set f'(x) equal to zero and solve for x:

[tex]4x^3 - 36x = 0[/tex]

Factor out 4x:

[tex]4x(x^2 - 9) = 0[/tex]

Now, set each factor equal to zero:

So, the critical points are x = 0, -3, and 3.

To determine whether each critical point corresponds to a minimum, maximum, or an inflection point, we can use the second derivative test. The second derivative is:

[tex]f''(x) = 12x^2 - 36[/tex]

Evaluate f''(x) at each critical point:

Therefore, at x = -3, the graph changes from decreasing to increasing.

Answer:

$98,636.72

Step-by-step explanation:

Given cosx = 4/5 and cscx < 0, we can find sin2x = -24/25, cos2x = 7/25, and tan2x = -3/8 using trigonometric identities.

To find sin2x, cos2x, and tan2x given cosx = 4/5 and cscx < 0, we can use trigonometric identities. First, let's find sinx using the Pythagorean identity: sinx = sqrt(1 - cos^2x) = sqrt(1 - (4/5)^2) = sqrt(1 - 16/25) = sqrt(9/25) = 3/5. Since cscx < 0, we know that sinx is negative. Therefore, we have sinx = -3/5.

Next, we can use the double angle identities to find sin2x, cos2x, and tan2x. The double angle identities state that sin2x = 2sinxcosx, cos2x = cos^2x - sin^2x, and tan2x = 2tanx / (1 - tan^2x).

Using the values we found earlier, we can calculate:

sin2x = 2(-3/5)(4/5) = -24/25

cos2x = (4/5)^2 - (-3/5)^2 = 16/25 - 9/25 = 7/25

tan2x = 2(-3/5) / (1 - (-3/5)^2) = -6/5 / (1 - 9/25) = -6/5 / (16/25) = -6/16 = -3/8

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The correct values for sin2x, cos2x, and tan2x given that cosx = 4/5 and cscx < 0 are as follows:

sin2x = -24/25

cos2x = 7/25

tan2x = -24/7

To find these values, we will use trigonometric identities and the given information.

First, since cosx = 4/5 and cosx is positive, we know that x must be in the first or fourth quadrant. However, because cscx < 0 (which means sinx is negative), x must be in the fourth quadrant since cscx is the reciprocal of sinx.

In the fourth quadrant, sinx is negative, so we can find sinx using the Pythagorean identity:

sin^2x + cos^2x = 1

sin^2x = 1 - cos^2x

sin^2x = 1 - (4/5)^2

sin^2x = 1 - 16/25

sin^2x = 25/25 - 16/25

sin^2x = 9/25

Since sinx is negative in the fourth quadrant, sinx = -3/5.

Now, we can use the double-angle identities to find sin2x, cos2x, and tan2x:

sin2x = 2sinxcosx

sin2x = 2 * (-3/5) * (4/5)

sin2x = -24/25

cos2x = cos^2x - sin^2x

cos2x = (4/5)^2 - (-3/5)^2

cos2x = 16/25 - 9/25

cos2x = 7/25

tan2x = sin2x/cos2x

tan2x = (-24/25) / (7/25)

tan2x = -24/7

Final answer:

The probability that it will rain today or tomorrow, given the individual probabilities and the joint probability for both days, is calculated using the addition rule of probability, resulting in a probability of 0.5 or 50%.

Explanation:

The student is asking how to calculate the probability that it will rain today or tomorrow given the individual probabilities for rain on each day and the joint probability that it will rain on both days. This is a typical question involving the addition rule of probability.

To find the probability of either event A (rain today) or event B (rain tomorrow) occurring, we use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

Where:

P(A) is the probability that it will rain today, which is 0.4,

P(B) is the probability that it will rain tomorrow, which is 0.3, and

P(A and B) is the probability that it will rain on both days, which is 0.2.

Substituting the given values, we get:

P(A or B) = 0.4 + 0.3 - 0.2

P(A or B) = 0.5

Therefore, the probability that it will rain today or tomorrow is 0.5, or 50%.

Answer:

50

Step-by-step explanation:

So 8 percent equals to 4 so just multiply the reciprocal of 8/100 and you get 50

slope = growth during 1 year y-intercept = their original height i.e. the height when they were born

The standard linear equation is given by :-

[tex]y=mx+c[/tex], where m is the slope and c is the y-intercept.

Given equation to predict the average height of boys anywhere b/w birth and 15 years old:

[tex]y=2.79x+25.64[/tex], where x is the age(in yrs) and y is the height (in inches).

By comparing this equation to the standard linear equation, we have

Slope = 2.79 and y-intercept = 25.64

The slope tells that the rate of change of average height of boys with respect to age is 2.79 .

The y-intercept tells that the initial average height of boys =25.64 inches

Both equations are two-step equations involving a variable term multiplied by a constant and then subtracting another constant. Peter's is 4x - 2 = 10 and Andres's is 16x - 8 = 40.

One way in which Peter's equation 4x - 2 = 10 and Andres's equation 16x - 8 = 40 are similar is that they both involve a variable term multiplied by a constant and then subtracting another constant.

In Peter's equation, 4x represents four times a variable x, and then subtracting 2 from the result.

Similarly, in Andres's equation, 16x represents sixteen times a variable x, and then subtracting 8 from the result.

This common structure of multiplying a variable term by a constant and then subtracting another constant makes both equations two-step equations, even though the specific values and constants differ.

Two triangles with the same corresponding side lengths will be congruent - False

False. Two triangles with the same corresponding side lengths are not guaranteed to be congruent. They may still be similar triangles with equal corresponding angles but different sizes.