which angle is conterminal with a 645 degree angle

a. an angle measuring 75 degrees
b. an angle measuring 265 degrees
c. an angle measuring 345 degrees
d. an angle measuring 285 degrees

Answer:

-7

Step-by-step explanation:

hope it helps

The (g.f)(x)  of the two functions is:

(g.f) (x) = 6x + 37

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

To find (g.f) (x), follow the steps below:

1. Substitute the value of f(x) into the function g(x).

2. Then simplify the expression.

That is:

f(x) = 3x+18

g(x) = 2x+1

Thus, we have:

(g.f) (x) = g(f(x))

(g.f) (x) = g(3x+18)

(g.f) (x) = 2(3x+18) + 1

(g.f) (x) = 6x+36 + 1

(g.f) (x) = 6x + 37

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Answer:

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

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

y - 1 = 3/2 (x + 3)

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-4)) / (2 - (-2))

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

y - 1 = (3/2)(x + 3)

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

y - 1 = 3/2 (x + 3)

Answer:

p=4375.00

Step-by-step explanation:

P=A / ( 1 + rt)

Answer:

20,000

Step-by-step explanation:

1=$5,600,r=4%+=7years

I=prt

5600=p(0.28)

5600/0.28=p(0.28)/0.28

Principal 20,000

The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.

1. The given function is f(x) = \(-2(x+4)^2\) + 1.

2. To find the maximum of the function, we need to determine the vertex of the parabola.

3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.

4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.

5. The x-coordinate of the vertex is given by h = -4.

6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.

7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.

8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).

9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.

10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.

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In the exponent form, the gold is worth approximately $ 5.76 × \(10^{21}\).

What are power and exponent?

In mathematical relationships, power refers to the number of times a number is multiplied by itself, i.e. the number obtained by raising a number to an exponent, whereas an exponent is the number of times the number is used in multiplication. Exponents are also referred to as powers or indices.

Given, The Earth's crust contains approximately 120 trillion metric tons of gold = 1.2 × \(10^{14}\) metric tons of gold

And, One metric ton of gold is worth $48 million = $ 4.8 × \(10^{7}\)

So, the value of the gold in the Earth's crust = 4.8 × \(10^{7}\)× 1.2 × \(10^{14}\)

                                                                         = 5.76 × \(10^{7+14}\)

                                                                         = $ 5.76 × \(10^{21}\)

Hence, the gold is worth approximately $ 5.76 × \(10^{21}\).

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Answer:c

Step-by-step explanation is va cuz when your multiply:

Answer:

\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)

Step-by-step explanation:

The analysis is as attached below.

Answer:

Step-by-step explanation:

prime factorization of 60= 2*2*3*5 = \(2^{2} * 3^{1} * 5^{1}\)

prime factorization of 150 = 2*3*5*5 = \(2^{1} * 3^{1} * 5^{2}\)

greatest (highest) common factor (divisor), calculated

HCF = 2*3*5 = 30

For LCM, when you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to

LCM = \(2^{2} * 3^{1} * 5^{2}\)=300

System Linear equation has no solution , because it is paralell lines but no intersection.

What is system linear equation?

An equation for a line is known as a linear equation. alternatively, y + 0.5x 3.5 = 0 and others. (Note that each linear equation is the same.) When multiple linear equations interact, we get a system of linear equations.

Here the given system linear equations,

\(3y=\frac{3}{2}x+6\) -------> 1    and \(\frac{1}{2}y-\frac{1}{4}x=3\) --------> 2

Divide by 3  of equation 1 on both sides then,

\(y=\frac{1}{2}x+2\)  -----------> 3

Now put 3 into 2 then,

=> \(\frac{1}{4}x+1-\frac{1}{4}x=3\)

=> 1=3

Hence the given system equation has no solution , because it is paralell lines but no intersection.

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Answer:

Brianna will earn 28 points for 1 level

Explanation:

Given that;

Brianna earned 56 points from two levels.

And the player earns equal points in each level.

Then for one level we have;

so, we have;

Therefore, Brianna will earn 28 points for 1 level

Answer:

1) m = 9/2, n = 9

3) x = y = (3√2)/2

Step-by-step explanation:

1) We have a 30°-60°-90° right triangle, so the length of the longer leg is √3 times the length of the shorter leg, and the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is (9√3)/2, so m, the length of the shorter leg, is 9/2, and n, the length of the hypotenuse, is 18/2, or 9.

3) We have an isosceles right triangle, so the length of the hypotenuse is √2 times the length of each leg. The length of the hypotenuse is 3, so x and y, the lengths of the two congruent legs, are 3/√2, or (3√2)/2.

Answer:

D. <S, <R, <T

Step-by-step explanation:

Recall: On a triangle, the bigger an angle measure the longer the side opposite it and vice versa.

In ∆RST,

The longest side, SR = 22, is opposite to <T

Therefore, <T is the biggest angle.

Medium side, ST = 21, is opposite to <R, therefore,

<R is the medium angle measure

The smallest angle measure <S is opposite to the shortest side, RT.

Angels I'm order form the smallest to largest will be:

<S, <R, <T

Answer:

I'm pretty sure it is

Step-by-step explanation:

Answer:

Volume is LxWxH so you will first do the bigger cube. count the squares you see for length, width, and hieght on the first cube so that will be:

10x9x5 which equals 450. Now we go to the cube that is on the bottom right that is attached to the other cube that is 450. Now we do the same with that.

5x9x2. And the volume for that will be 90.

Since we just figured out these cubes, we add these two together

450+90=540

The answer is 540. Have a great day, and i hope this helped :)

Using the distributive property to write sum as a product with two factors gives:

a.  9a

b. 5(z - 2)       

c. c (1 - 2c)

d. 4r

e. 2 (x - 1/4)

The distributive property is a property of multiplication that allows us to break up an expression into smaller parts that can be added or subtracted.

To use the distributive property to write a sum as a product with two factors, we need to identify a common factor between the terms in the sum. Then, we can factor out that common factor and apply the distributive property.

a. 2a +7a = (2 + 7) a

                = 9a

b. 5z - 10 = 5(z - 2)

c. c-2c² = c (1 - 2c)

d. r + r + r + r = 4r

e. 2x - 1/2 = 2 (x - 1/4)

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Answer:

(1/2)x+(1/4)=x

x=0.5

3x+3=2(x+7)

x=11

2(x-5)+7=x+8

x=11

0.8x+5=0.2(40-x)

x=3

5(x-1)-6x=-11x

x=0.5

6(x+2)-x=4(x+4)+7

x=11

(1/2)(x+8)+(3/2)x=10

x=3

Step-by-step explanation:

(1/2)x+(1/4)=x

x-0.5x=0.25

0.5x=0.25

x=0.5

3x+3=2(x+7)

3x+3=2x+14

3x-2x=14-3

x=11

2(x-5)+7=x+8

2x-10+7=x+8

2x-x=8+10-7

x=11

0.8x+5=0.2(40-x)

0.8x+5=8-0.2x

0.8x+0.2x=8-5

x=3

5(x-1)-6x=-11x

5x-5-6x=-11x

11x-x=5

10x=5

x=0.5

6(x+2)-x=4(x+4)+7

6x+12-x=4x+16+7

6x-4x-x=16+7-12

x=11

(1/2)(x+8)+(3/2)x=10

0.5x+4+1.5x=10

2x=6

x=3

Answer:

605

Step-by-step explanation:

11x55=605

Answer:

Greg used 1/10 more meters

Step-by-step explanation:

3/5=6/10

1/2=5/10

Answer:

1/10

Step-by-step explanation:

3/5 - 1/2

then we multiply to make the denominator even

6/10-5/10

ANSWER = 1/10

Answer:

It is C sorry if im wrong :)

Step-by-step explanation:

Hello! :)

\(\large\boxed{\text{Linear.}}\)

The function pictured is a straight line, so it has a constant slope for all x values.

A function that has the same slope on its domain and when graphed is a straight line is a linear function.

Probability that it is Saturday is 1/2 as it is on weekend. We can calculate this using Conditional Probability formula.

Given that a day of the week is randomly selected and that it is on the weekend, the probability of it being Saturday can be calculated as follows:

There are two days in a week that are on the weekend: Saturday and Sunday.

If we know that a day is on the weekend, the probability of it being Saturday is equal to the number of Saturdays on the weekend divided by the total number of weekend days. This is because there are two equally likely outcomes for the weekend (Saturday and Sunday), and we are interested in only one of them.

We can find this out by using formula:

P(A|B) = P(A and B) / P(B), where A and B are two events.

So, the probability of selecting Saturday, given that it is on the weekend, is 1/2. In other words, if we randomly select a day of the week and it is on the weekend, there is a 50% chance that it will be Saturday.

This can be written as P(Saturday|Weekend) = 1/2.

Therefore, probability = 1/2

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The linear equation can be written as:

y = (3/4)*x + 17/4

And the graph can be seen at the end.

A general linear equation is of the form:

y = m*x + b

Where m is the slope and b is the y-intercept.

Here we have the slope m = 3/4, so we get:

y = (3/4)*x + b

And the line passes through (1, 5), replacing these values in the equation we get:

5 = (3/4)*1 + b

5 - 3/4 = b

20/4 - 3/4 = b

17/4 = b

So the linear equation is:

y = (3/4)*x + 17/4

To graph the line we need other point, if we use x = 0 we get:

y = (3/4)*0 + 17/4 = 17/4

Then we have the points (1, 5) and (0, 17/4).

To graph the line, we just need to find these two points and connect them with a line, the graph can be seen below.

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The midpoint of three points with the position vector 1/3(a + b + c) is given by:

P = (b + c - B - C) / 2 + (1/3)(b + c)

The point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

To find the point with the position vector 1/3(a+b+c), we can use the fact that the position vector of a point that divides a line segment in a given ratio can be found by taking the weighted average of the position vectors of the endpoints.

Given that D, E, and F are the midpoints of line segments BC, AC, and AB, respectively, we know that:

D = (B + C) / 2

E = (A + C) / 2

F = (A + B) / 2

To find the point with the position vector 1/3(a+b+c), we can substitute a = 3F - 2D - E into the equation:

1/3(a + b + c) = 1/3((3F - 2D - E) + b + c)

Expanding the equation further:

1/3(a + b + c) = 1/3(3F - 2D - E + b + c)

= (F - (2/3)D - (1/3)E) + (1/3)(b + c)

Therefore, the point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

Substituting the midpoints:

P = (A + B) / 2 - (2/3)((B + C) / 2) - (1/3)((A + C) / 2) + (1/3)(b + c)

= (A + B - 2B - 2C - A - C + b + c) / 2 + (1/3)(b + c)

= (b + c - B - C) / 2 + (1/3)(b + c)

Therefore, the midpoint of three points with the position vector 1/3(a + b + c) is given by:

P = (b + c - B - C) / 2 + (1/3)(b + c)

The point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

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Answer:

---------------------

Formula for area of a rectangle with dimensions l and w is:

Substitute 10 for l and 4 for w:

Step-by-step explanation:  

So... where it says Y=4x-1, take the 4x and plot it on the y axis, next on the equation it says -1, plot -1 on the left ( X-axis)

I hope this helps

Answer:

\(b  =  (q,r , 5q-2\sqrt{26} )\)

Step-by-step explanation:

From the question we are told that

The vector given is  

               \(a = (5,0,-1)\)

  Also  \(comp_a b =  2\)

Generally

       \(comp_a b  =  \frac{a \cdot b}{|a|}\)

Here  \(|a|\) is the magnitude of  a which is mathematically represented as

      \(|a| =  \sqrt{5^2  + 0^2  +(-1)^2 }\)

=>     \(|a| =  \sqrt{26}\)

b is vector which we will assume to have the following parameters

     \(b  =  (q , r , x)\)

So

        \(comp_a b =  \frac{(5,0,-1) \cdot (q,r,x)}{\sqrt{26} } =  2\)

=>     \(\frac{5q + 0 -x}{\sqrt{26} } = 2\)

=>     \(x =  5q-2\sqrt{26}\)

Hence the vector be can be mathematically represented as

      \(b  =  (q,r , 5q-2\sqrt{26} )\)

This means that the vector b is more than one value  since it is made up of variable

This means that if

   \(q = 1\\r=1\\x =1\)

Then

    \(b  =  (1,1,5-2\sqrt{26} )\)

A quantity has magnitude but not position, that's why in this the vector \(b =(0,0, -2\sqrt{26}).\)

If\(a =(5,0,-1)\) Our goal is to determine a vector b that will allow comp to work properly \(_{a}b = 2.\)

Allow the vector to flow naturally  \(b =(x, y,z)\)

Recalling

comp\(_{a}b =\frac{a.b}{|a|}\)

Therefore,

comp \(_{a}b= 2 \\\\\)

\(\to \frac{a.b}{|a|}= 2\\\\\)

\(\to \frac{(5,0,-1)\cdot (x,y,z)}{ |(5,0,-1)|} =2\\\\\to \frac{5x+0-z}{5^2+0+(-1)^2}=2\\\\ \to \frac{5x-z}{\sqrt{26}}= 2 \\\\\to 5x-z = 2\sqrt{26}\\\\ \to z=5x-2\sqrt{26}\\\\\)

As a result, the vector b can be expressed as,

\(\to b =(x,y,z) =(x, y, 5x-2\sqrt{26}) \\\\\)

As a result, this aforementioned form can be found in an endless number of vectors.

One of them is \(b =(0,0, -2\sqrt{26}).\)

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The solution for the given expression is 16.

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

First, you apply the Power Rules - Power for  \((\frac{2^2x^2y}{xy^3} )^2}\). For this rule, you should repeat the base and multiply the exponents. Thus, the result will be:\(\frac{16x^4y^2}{x^2y^6}\).

After that, you should apply the  Power Rules - Division . For this rule, you should repeat the base and  subctract the exponents. Thus, the result will be:\(\frac{16x^2}{y^4}\).

Now, you should replace the variable x by 4 and the variable y by 2. Thus, the result will be:\(\frac{16*4^2}{2^4}=\frac{16*16}{16} =16*1=16\)

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