Sketch a diagram of a 315° angle in standard position and indicate the measure of its reference angle.

translation means moving a geometric object in the cartesian plane without rotating it.

In they are orthogonal the their scarlar product will be zero.

So

Hence, [tex]y=11.714[/tex] when the [tex]a[/tex] and [tex]b[/tex] are orthogonal.

What is the vectors?

Vectors in math is a geometric entity that has both magnitude and direction. Vectors have an initial point at the point where they start and a terminal point that tells the final position of the point.

Various operations can be applied to vectors such as addition, subtraction, and multiplication.

Here given that,

[tex]a=(9,-7,-7)\\b=(6,y,-4)[/tex]

If they are orthogonal the their scarlar product will be zero.

So,

[tex](9,-7,-7).(6,y,-4)=0\\54-7y+28=0\\-7y=-82\\As,\\a.b=0\\y=\frac{82}{7}\\y=11.714[/tex]

Hence, [tex]y=11.714[/tex] when the [tex]a[/tex] and [tex]b[/tex] are orthogonal.

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We were told that Aubrey paints 4 square feet of her house each minute.

Recall that 1 minute = 60 seconds.

The statement can be written as

Aubrey paints 4 square feet of her house each 60 seconds

If x represents the number of square feets that she paints in 20 seconds, it means that

4 = 60

x = 20

By cross multiplying, it becomes

60 * x = 4 * 20

60x = 80

x = 80/60

x = 1.333

Rounding to the nearest tenth, it becomes 1.3 square feet

She paints 1.3 square feet in 20 seconds

f(1) = 10

Given f(x) = 3x + 7

To find f(1), replace x by 1 in the equation above

f(1) = 3(1) + 7

= 3 + 7

= 10

The slope-intercept form of the line is

where m is the slope and b is the y-intercept

so we only need to substitute the values into the equation

m=2

b= -5

the equation is

First, we need to find the slope of the line:

Let:

(5, -4) = (x1,y1)

(-9, -8) = (x2,y2)

m = (y2-y1)/(x2-x1) = (-8-(-4))/(-9-5) = -4/-14 = 2/7

Also, we need to find the midpoint:

let:

MP = (xp,yp)

xp= (x1+x2)/2 = (5-9)/2 = -2

yp = (y1+y2)/2 = (-4-8)/2 = -6

MP = (-2, -6)

Now, the slope for the perpendicular bisector is -m = -7/2

y = -mx + b

Using the midpoint

-6 = -7/2(-2) + b

-6 = 7 + b

Solving for b:

b = -13

Therefore, the equation for the perpendicular bisector is:

y = -7x/2 - 13

EXPLANATION

Given the equation y = -2.5x + 92

The slope is equal to -2.5

Given the graph represents the amount of water in the aquarium versus time.

A) As shown in the graph :

as the time increases the amount of water in the aquarium decreases

The rate of water decreasing =

so, the rate = 60 litres per minute

The APR, that is Annual Percentage Rate, is calculated using the formula below;

Answer:

Explanation:

Here, we want to know the table that represents a function

For a relationship to represent a function, no two y values can have a single x value but two x values can have a single y value.

What this means is that two independent variable values can take a single dependent variable value but no two dependent variable values can take a single independent variable value

Now, looking at the table given:

The diagram below shows all the possible outcomes from rolling a pair of six sided dice.

The first row and first columns represents the numbers on each die. The numbers in the other rows and columns are outcomes for each roll. Thus, the total number of outcomes is the total number of pairs in the other rows and columns.

Total number of outcomes = 36

Number of outcomes with sum greater than or equal to 11 are the circled pairs. They are 3

Thus, the probability of rolling a sum greater than or equal to 11 is

3/36 = 1/12

SOLUTION

Density is calculated as

The side lengths of the aluminium cube has been given as 0.5 m

The volume becomes

so the volume is 0.125 cubic-meters.

The mass becomes

Hence the answer is 337.5 kg

To find the acale factor we need to solve the following equation:

This comes from the fact that the biggest sides of both triangles have to be realted.

Therefore the dilation factor is 0.4.

The AAS triangle congruence postulate proves that these triangles are congruent .

In the question,

two triangles are given that are triangle ABC and triangle PQR .

Consider the triangle ABC and triangle PQR .

we can see that

(i) angle C = angle R           .....given in the figure

(iii) angle B = angle Q         .... given in the figure

(ii) side BC = side QR          ....given in the figure

From the above three statements we conclude that

ΔABC ≅ ΔPQR

both the triangles KLM and PQR are congruent by AAS Congruence Postulate .

Therefore , The AAS triangle congruence postulate proves that these triangles are congruent .

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We have that:

• A randomly generated list of, integers from 0 to 4 i,s being used to simulate an event.

• The number 3 represents a success.

And we need to find the estimated probability of success.

We can achieve that if we know that:

1. We have the following sample space for the experiment - we have a list of integers from 0 to 4:

2. Then the probability of having a 3 is:

We have one possibility of getting a 3 (one possibility) out of 5 possibilities (0, 1, 2, 3, 4).

Therefore, the estimated probability of success is 20% (option D.)

To study population growth, we use the following formula

Where,

Let's replace the values above, and solve for t.

Grace wants to bring a small wedge of cheese for the next 12 days, but there are three small rounds of cheddar cheese in Grace's refrigerator, That is to say, that Grace needs to buy cheese to fulfill this purpose, the small wedge of cheese that Grace needs are:

but we must represent this infraction, for this, we will take the 12 small wedges of cheese as a unit, which is formed by having the 12 portions.

That is, out of 12/12 portions, we only have 3/12, To do this we do subtraction and see how many we need in fractional form.

In conclusion, Grace need 9 portions i.e. 9/12

Now, that we know this fraction, this is a correct answer, however, we can simplify this fraction.

In conclusion, Grace needs 3/4 small wedge of cheese.

Note: the answer can be 9/12, but also its simplified form which corresponds to the same, this simplified form is 3/4.

We know that two jets leave Harrisburg at the same, time, one flying east, and another flying west.

We will denote the speed of the second jet by x (in km/h). Thus, the speed of the first jet is x+20. Remembering that:

where v is speed, d is distance and t is time, we know that for the first jet:

Where d₁ represents the distance of the first jet from the starting point. For the second jet:

Where d₂ represents the distance of the second jet from the starting point.

We also know that:

As:

Thus, we have that:

This means that the second jet has a speed of 740km/h, and the first jet has a speed of 760km/h (20km/h greater than the second one).

In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?

The equation 4x +8=28 could be used to describe a scenario like this below:

In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?

Notice the fixed amount (8) and the variable (4x) and the total of money you have (28). So the sum above describes the amount of money for that club.

With that equation you can find that:

4x +8=28

4x+8 -8 =28-8

4x=20

x=5

5 cans of soda.

The given points are (10, -3) and (5, -4).

The midpoint formula is

Where,

Replacing these coordinates, we have

Answer:

Yes, they are similar.

Criterion: AA Similarity

Explanation:

Looking at triangles YPQ and NPD, we can see that angles NPD and YPQ are vertically opposite angles and are congruent since vertically opposite angles are always congruent;

We can also observe that angles N and Y are congruent since they are alternate angles;

From the AA similarity rule, we know that two triangles are said to be similar if two angles in one triangle are equal to two triangles in the other triangle.

Therefore, from the AA rule, we can say that triangles YPQ and NPD are similar.

1) Let's visualize it to better understand:

A right rectangular prism is made from

2 faces 6 x 7

4 faces 20 x 6

Since we have rectangles, we can write calculating the area of each rectangle.

S base = 2 (6x 7) ⇒ S base = 84 cm²

S faces = 2 (20 x 6) ⇒ S faces = 240 cm²

S faces = 2 (20 x 7) ⇒ S faces = 280 cm²

2) Then the total surface area

84+240+280=604 cm²

By rotating the shape of the graph, we get the following cylinder:

So we have a cylinder with:

• radius r = 4,

• height h = 6.

The volume of the cylinder using π = 3.14 is given by:

The solid obtained is a cylinder of volume 301.44.

Given that A, B, and C are collinear and B lies between A and C, then:

AB + BC = AC

Replacing with data:

(2x + 2) + (3x + 6) = 48

(2x + 3x) + (2 + 6) = 48

5x + 8 = 48

5x = 48 - 8

5x = 40

x = 40/5

x = 8

Then,

BC = 3x + 6

BC = 3(8) + 6

BC = 24 + 6

BC = 30

The point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1) - 1.

The point-slope form is simply writing an equation of a line so that the slope or steepness and x-intercept i.e. where the line crosses the vertical x-axis are immediately apparent.

The slope-intercept equation is y - y1 = m(x - x1), where x and y are two variables, and m is the slope.

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

Let,

(x1, y1) = (-1, -1)

(x2, y2) = (2, 4)

Slope (m) = ((4) - (-1)) / ((2) - (-1))

                = 5/3

y - y1 = m(x - x1) => (y - (-1)) = 5/3(x - (-1))

                         => y+1 = 5/3(x + 1)

                         =>y = 5/3(x+1)-1

Therefore, the point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1)-1.

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We have the following data

The standard deviation is given by

Where μ is the mean and N is the number of data points

Let us first find the mean of the data.

Finally, the standard deviation is

Therefore, the standard deviation of the data set is 8.5

Solution:

The future price p(t), in dollars, can be modelled by the exponential function;

(a) The current price is;

ANSWER: $800

(b) The price 8 years from today;

ANSWER: $975

Probability = number of required outcome/number of the possible outcome

(a) To determine the theoretical probability for mary

(b) To determine the experimental probabiity for mary's result

(c) Assuming the spinner is fair, with a large number of spins there might be a difference between the experimental and theoretical probability but the difference will be small.

Ok ,we need to find p in the following equation: 2/5+p=4/5+3/5p, lets