5. Given: Line segment AD bisects

The direction of the resultant vector is approximately 320°.

We have three vectors. The magnitudes of the vectors t, u, and v are 7, 10, and 15, respectively. The angles of the vectors t, u, and v are 240°, 30°, and 310°, respectively. We have to find the angle of the resultant vector of the sum of all three vectors. To add all the three vectors, we need to split the vectors into their horizontal and vertical components. The horizontal components are 7cos(240°), 10cos(30°), and 15cos(310°). The vertical components are 7sin(240°), 10sin(30°), and 15sin(310°).

Let the horizontal and vertical components of the resultant vector be denoted by H and V, respectively. The horizontal component is H = 7cos(240°) + 10cos(30°) + 15cos(310°) = 7*(-0.5) + 10*(0.866) + 15*(0.643) = -3.5 + 8.66 + 9.645 = 14.805. The vertical component is V = 7sin(240°) + 10sin(30°) + 15sin(310°) = 7*(-0.866) + 10*(0.5) + 15*(-0.766) = -6.062 + 5 - 11.49 = -12.552. The angle of the resultant vector can be calculated by the ratio of the components as tan(θ) = V/H = -12.552/14.805 = -0.848. So, the angle "θ" is approximately equal to 320°.

To learn more about vectors, visit :

https://brainly.com/question/13322477

#SPJ9

Given:

Given that a figure Q and its transformation R.

Required:

To choose the correct transformation of the given figure.

Explanation:

The figure R is 7 unit right to the figure Q.

Therefore the option B is correct.

Final Answer:

(B) A translation of 7 units to the right.

32 miles ---------> 1 gallon

30 miles--------------> xgallons

Solving for x:

32/30 = 1/x

x = 30/32 = 0.9375 gallons

1 gallon ------>$2.55

0.9375 gallons----->$y

1/0.9375 = 2.55/y

Solving for y:

y = 2.55*0.9375 = $2.390625

It will cost $2.390625

The surface area is the sum of all the areas in the given prims, then we have:

Plugging the value for the surface area and silving for A we have:

Now that we know the missing area we can know the missing dimension:

Therefore the missing length is 12.

Divide the distance over the total time to find the distance Julia rides in one hour:

Do the same for each option to find whether or not they represent the same speed:

A)

B)

C)

D)

Therefore, only options B and C represent the same ratio.

given expression:

To find the value of n.

Answer:

1/4

Step-by-step explanation:

In total, there are 4 suits of cards: spades, clubs, hearts, and diamonds.

This way, the probability of drawing a heart from a standard deck of cards is:

Given the function:

Let's determine the range of the function using the graph.

The range of a function is the set of all possible y-values which define the function.

From the graph shown, the value of y starts from the vertex at y = -9 and goes upward.

Therefore, the range of the function is all values of y greater than or equal to -9.

{y|y ≥ - 9}

Hence, in interval notation is:

ANSWER:

Slope intercept form:

y= mx+ b

Where:

m= slope

b= y-intercept

For: y=-7x+5

m= -7

Perpendicular lines have negative inverse slopes.

Negative inverse of -7 = 1/7

So far we have

y= 1/7x + b

Replace (x,y) fo the given point (0,0) and solve for b:

0= 1/7(0) + b

b= 0

Final equation:

y= 1/7x

Answer: 8

Step-by-step explanation: if you add -2 and 8 you get 6.  :) pls give me brainliest

Explanation

In order to be able to predict the time, it will take to cover 220 miles, we will have to get the relationship

The relationship between distance and the time can be obtained as follow:

When the distance is 80 miles, the time taken is 2 hours

So when the distance is 220 miles, the time taken will be

Therefore, it will take 5.5 hours to cover a distance of 220 miles

Therefore, the answer is 5.5 hours

Given that

The Pythagoras theorem is true for all right triangles or not.

Explanation -

For each and every right-angled triangle the Pythagoras theorem can be used.

To answer this question, we need to recall that: "the diagonals of a parallelogram bisect each other"

Thus, we can say that:

And since: DE = 3x - 3 , and EB = x + 11, we have tha:

we now solve the above equation to find x, as follows:

Therefore, the correct answer is: option D

The function [tex]log_{b} \sqrt[3]{(\frac{x^{8} }{y^{9} z^{6} })}[/tex] is simplified to be [tex]8/3log_{b}x-3log_{b}y-2log_{b}z[/tex]

The function is simplified using the laws of logarithm

[tex]log_{b} \sqrt[3]{(\frac{x^{8} }{y^{9} z^{6} })}[/tex]

[tex]= log_{b}(\frac{x^{8} }{y^{9} z^{6} })^{1/3}[/tex]

[tex]= log_{b}(\frac{x^{8/3} }{y^{9/3} z^{6/3} })[/tex]

[tex]= log_{b}(\frac{x^{8/3} }{y^{3} z^{2} })[/tex]

Applying the quotient rule

[tex]= log_{b}x^{8/3}-log_{b}( y^{3} z^{2})[/tex]

Applying the product rule

[tex]= log_{b}x^{8/3}-(log_{b}y^{3}+log_{b}z^{2})[/tex]

expanding the parenthesis

[tex]= log_{b}x^{8/3}-log_{b}y^{3}-log_{b}z^{2}[/tex]

Applying the exponential rule

[tex]= 8/3log_{b}x-3log_{b}y-2log_{b}z[/tex]

Learn more about logarithm rules at:

https://brainly.com/question/29420555

#SPJ1

Answer:

3. √74

Explanation:

By the Pythagorean theorem, the length of the hypotenuse can be calculated as:

Where c is the hypotenuse and a and b are the lengths of the legs.

So, replacing a by 5 and b by 7, we get:

Therefore, the answer is 3. √74

Substitute a for x

Determine - f(a) for f(x) =2x/x-1 and simplify.​

Thus, the solution becomes:

Answer:

How to write 476 in scientific notation.

To write a number in scientific notation, express the number in the form:

Where m is a number that has a unit place value. (That is a number less than 10 but greater than 1)

In the case of 476, you put a point after 4, you would see that there are two digits after 4 ( 7 and 6)

The scientific notation of 476 is therefore:

To factor the above quadratic equation using Earmuff Method, here are the steps:

1. Multiply the numerical coefficient of the degree 2 with the constant term.

2. Find the factors of 24 that when added will result to the middle term 10.

1 and 24 = 25

2 and 12 = 14

3 and 8 = 11

6 and 4 = 10

Upon going over the factors, we will find that 6 and 4 are factors of 24 and results to 10 when added.

3. Add "x" on the factors 6 and 4. We will get 6x and 4x.

4. Replace 10x in the original equation with 6x and 4x.

5. Separate the equation into two groups.

6. Factor each group.

7. Since (x + 2) is a common factor, we can rewrite the equation into:

Hence, the factors of the quadratic equation are (3x + 4) and (x + 2).

Another way of factoring quadratic equation is what we call Slide and Divide Method. Here are the steps.

1. Slide the numerical coefficient of the degree 2 to the constant term by multiplying them. The equation becomes:

2. Find the factors of 24 that results to 10 when added. In the previous method, we already found out that 6 and 4 are factors of 24 that results to 10 upon adding. So, we can say that the factors of the new equation we got in step 1 is:

3. Since we slide "3" to the constant term, divide the factors 6 and 4 by 3.

4. Since we can't have a fraction as a factor, slide back the denominator 3 to the term x in the same factor.

Similarly, we got the same factors of the given quadratic equation and these are (x + 2) and (3x + 4).

We can use the compound interest formula:

Where:

A = Amount = $37000

P = Principal

r = Interest rate = 9% = 0.09

n = Number of times interest is compounded per unit of time = 4 (Since it is compounded quarterly)

t = time = 18

Therefore:

Solve for P:

ANSWER:

33.5%

STEP-BY-STEP EXPLANATION:

We have the amount in 2003 in 5799 fish and in 2014 there are there are 1943 less fish.

The percentage of change would be the difference in fish between these years divided by the initial amount of fish, just like this:

This means that the percentage of change is negative since the population has decreased by 33.5%.

It is important to know that the gound level is zero, so the bone is closer to the ground level because -4.5 is closer than -12.5 or 4.5.

The only rigid motion that could be used to show that angle BAE is congruent to the angle DAC is D.

Because if we do the rotation of 180° clockwise about A we will obtain the same Figure.

This is the original figure

As we can see making the rotation we obtain same figure

To answer this question, we have to convert the given amount of barrels to feet and to inches using the conversion factors shown.

Barrels to feet:

Barrels to inches:

It means that the total amount deposited would be 3.04 ft or 36.47 in.

Given:

Common ratio=-3

11th term=11

To determine the 13th term, we first note the geometric sequence formula:

where:

a=1st term

n=nth term

Since the 11th term is 11, we can solve the first term by following the process as shown below:

Next, we plug in a=11/59049 when n=13:

Therefore, the answer is: 99

Odds in favor of receiving a gift = 5/13

The probability of receiving a gift, P(R) = 5/18

Probability of not receiving a gift, P(nR) = 1 - 5/18 = 13/18

The odds in favor of receiving a gift is calculated below:

Therefore:

Odds in favor of receiving a gift = 5/13

For the long-distance service, David pays a monthly fee of $7 plus 7 cents per minute.

Let "d" represent the minutes the call lasted, and "c" the total cost of the bill, then you can express the total cost of the bill using the following expression:

If the total cost of the bill was c=13.93, to determine the number of minutes David was billed for, you have to replace input this value in the equation and solve it for d

Pass 7 to the other side of the equation by applying the opposite operation

And divide both sides by 0.07 to determine the value of d

David was billed for 99minutes.

The first answer is: definition of complementary angles.

The second is: of the triangle sum theorem.

The third one is: substraction property

Let t = time traveled at 51 mph

The total time is given as 3.5 hours

So (3.5- t )= time traveled at 62 mph

We are going to use the distance formula:

distance = speed* time

51t + 62(3.5-t) = 200.5

51t + 62*3.5 - 62*t = 200.5

51t + 217 - 62t = 200.5

Solve the equal terms

51t - 62t = 200.5 - 217

-11t = -16.5

t = -16.5/-11

t = 1.5

Then he took 1.5 at 51mph

and (3.5- t ) = (3.5-1.5) = 2h at 62 mph

To confirm these results, find the actual speed of each speed:

speed* time = distance

51*1.5 = 76.5miles

62*2. = 124 miles

76.5miles + 124 miles = 200.5miles

Answer: Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect.

bruce will charge the customer $23.75

Explanation:

Amount charged per pound = $4.75

Let the number of pounds of produce = x

Total cost per number of pounds = $4.75 × x

Let the total cost of produce = y

y = 4.75x

If the number of pounds of produce = x = 5

y = 4.75 (5)

y = $23.75

Therefore, bruce will charge the customer $23.75