A line passes through the points (1, –6) and (4, 3).


What is the y-intercept of this line?
–9
–3
3
9

HG^2 = FG * (FG + EF)

Fill in the values:

(x+3)^2 = x * (7+x)

Simplify the right side:

(x+3)^2 = 7x +x^2

Rewrite the left side using the FOIL method

x^2 + 6x + 9 = 7x +x^2

Subtract x^2 from both sides:

6x +9 = 7x

Subtract 6x from both sides:

x = 9

Now you have x solve for HG

HG = x +3 = 9+3 = 12

The answer is A.

Answer:

When proving identities, the answer is in the explanation.

Step-by-step explanation:

[tex]\frac{\cos(y)}{1-\sin(y)}[/tex]

I have two terms in this denominator here.

I also know that [tex]1-\sin^2(\theta)=\cos^2(theta)[/tex] by Pythagorean Identity.  

So I don't know how comfortable you are with multiplying this denominator's conjugate on top and bottom here but that is exactly what I would do here.  There will be other problems will you have to do this.

[tex]\frac{\cos(y)}{1-\sin(y)} \cdot \frac{1+\sin(y)}{1+\sin(y)}[/tex]

Big note here: When multiplying conjugates all you have to do is multiply fist and last.  You do not need to do the whole foil.  That is when you are multiplying something like [tex](a-b)(a+b)[/tex], the result is just [tex]a^2-b^2[/tex].

Let's do that here with our problem in the denominator.

[tex]\frac{\cos(y)}{1-\sin(y)} \cdot \frac{1+\sin(y)}{1+\sin(y)}[/tex]

[tex]\frac{\cos(y)(1+\sin(y))}{(1-\sin(y))(1+\sin(y)}[/tex]

[tex]\frac{\cos(y)(1+\sin(y))}{1^2-\sin^2(y)}[/tex]

[tex]\frac{\cos(y)(1+\sin(y))}{1-\sin^2(y)}[/tex]

[tex]\frac{\cos(y)(1+\sin(y))}{cos^2(y)}[/tex]

In that last step, I apply the Pythagorean Identity I mentioned way above.

Now You have a factor of cos(y) on top and bottom, so you can cancel them out.  What we are really saying is that cos(y)/cos(y)=1.

[tex]\frac{1+\sin(y)}{cos(y)}[/tex]

This is the desired result.

We are done.

Answer:

A

Step-by-step explanation:

The line is divided into 9 parts between 1 and 2

A is situated 6 parts of the way between 1 and 2, that is

[tex]\frac{6}{9}[/tex] = [tex]\frac{2}{3}[/tex] ← cancelling by 3

Hence

A = 1 + [tex]\frac{2}{3}[/tex] = 1 [tex]\frac{2}{3}[/tex] → A

Answer:

Step-by-step explanation:

[tex]\text{The formula of a distance between x and y on a number line:}\\\\d=|b-a|=|a-b|\\\\\text{We have}\ a=\dfrac{5}{2}\ \text{and}\ b=4\dfrac{7}{8}.\ \text{The distance:}\\\\d=\left|\dfrac{5}{2}-4\dfrac{7}{8}\right|=\left|4\dfrac{7}{8}-\dfrac{5}{2}\right|}[/tex]

Answer:

none of the above

Step-by-step explanation:

Step-by-step explanation:

m∠3 + m∠4 = 180°

TRUE - they are supplementary angles

m∠2 + m∠4 + m∠6 = 180°

TRUE - measureas of angles in a triangle add up to 180°

m∠2 + m∠4 = m∠5

TRUE, because

m∠2 + m∠4 + m∠6 = 180° and m∠6 + m∠5 = 180°

therefore m∠2 + m∠4 + m∠6 = m∠6 + m∠5   subtract m∠6 from both sides

m∠2 + m∠4 = m∠5

m∠1 + m∠2 = 90°

FALSE, because m∠1 + m∠2 = 180°

m∠4 + m∠6 = m∠2

FALSE, because

m∠4 + m∠6 + m∠2 = 180°     subtract m∠2 from both sides

m∠4 + m∠6 = 180° - m∠2

m∠2 + m∠6 = m∠5

FALSE, because

m∠5 + m∠6 = 180°          subtract m∠5 from both sides

m∠6 = 180° - m∠5      add m∠2 to both sides

m∠2 + m∠6 = 180° - m∠5 + m∠2

Answer:

sin^-1 (1/2) = 30°

Step-by-step explanation:

* Lets explain how to find the trigonometry functions from the unit circle

- The unit circle is the circle whose radius is 1 unit

- It intersects the four axes at:

# Positive part of x-axis at (1 , 0) and negative part at (-1 , 0)

# Positive part of y-axis at (0 , 1) and negative part at (0 , -1)

- The terminal of any angle intersect it at point (x , y) where x² + y² = 1

- If The angle between the terminal side and the x-axis is Ф , then

# The adjacent side of Ф = x

# The opposite side of the angle Ф = y

- In the problem the terminal side lies in the first quadrant

∴ all the trigonometry functions are positive

∵ sin Ф = opposite/hypotenuse

∵ The opposite = 1/2 and the hypotenuse is the terminal side = 1

∴ sin Ф = 1/2 ÷ 1 = 1/2

- To find Ф use the inverse function sin^-1 Ф

∵ sin Ф = 1/2

∴ Ф = sin^-1 (1/2)

∴ Ф = 30°

* sin^-1 (1/2) = 30°

Answer:

You should choose an account with a 7% annual interest rate which is compounded quarterly

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

part 1)

we have  

[tex]t=15\ years\\ P=\$14,000\\ r=0.07\\n=4[/tex]  

substitute in the formula above  

[tex]A=14,000(1+\frac{0.07}{4})^{4*15}[/tex]

[tex]A=14,000(1.0175)^{60}[/tex]  

[tex]A=\$39,645.43[/tex]  

part 2)

we have  

[tex]t=15\ years\\ P=\$14,000\\ r=0.068\\n=12[/tex]  

substitute in the formula above  

[tex]A=14,000(1+\frac{0.068}{12})^{12*15}[/tex]

[tex]A=14,000(1.0057)^{180}[/tex]  

[tex]A=\$38,713.11[/tex]  

Answer:

x=1

Step-by-step explanation:

1) 6x-5y=5

2) 3x+5y=4

ets perform the following operation

1) +2), This leads to the following equation:

6x+3x-5y+5y=5+4

From where we obtain the solution for x

9x=9

x=1

Answer:

Slope: [tex]\frac{3}{5}[/tex]

Y-intercept: -3

Equation: [tex]y=\frac{3}{5} x-3[/tex]

Graph is attached.

Step-by-step explanation:

To find your slope using two points, use the slope formula.

[tex]\frac{y2-y1}{x2-x1} \\[/tex]

Your y1 is -6, your y2 is 3.

Your x1 is -5, your x2 is 10.

[tex]\frac{3-(-6)}{10-(-5)} \\\\\frac{9}{15} \\\\\frac{3}{5} \\[/tex]

Now that you have your slope, use it and one of your points in point-slope form to find your y-intercept.

[tex]y-y1=m(x-x1)\\y-3=\frac{3}{5} (x-10)\\y-3=\frac{3}{5} x-6\\y=\frac{3}{5} x-3[/tex]

Answer:

A. In the graph,

Go 5 units left side from the origin in the x-axis then from that point go downward 6 unit, we will get (-5, -6),

Now, go 10 unit right from the origin in the x-axis then from that point go upward 3 unit, we will get (10, 3),

B. The slope of the line passes through (-5, -6) and (10, 3),

[tex]m=\frac{3-(-6)}{10-(-5)}=\frac{3+6}{10+5}=\frac{9}{15}=\frac{3}{5}[/tex]

C. Since, the equation of a line passes through [tex](x_1, y_1)[/tex] with slope m is,

[tex]y-y_1=m(x-x_1)[/tex]

Thus, the equation of the line is,

[tex]y+6=\frac{3}{5}(x+5)----(1)[/tex]

For y-intercept,

x = 0,

[tex]y+6 = \frac{3}{5}(0+5)\implies y = 3-6=-3[/tex]

That is, y-intercept is -3.

D. From equation (1),

[tex]5y + 30 = 3x + 15[/tex]

[tex]\implies 3x - 5y = 15[/tex]

Which is the required linear function.

So, the inequality in slope-intercept form is [tex]\( y \geq 2x - 15 \).[/tex]

To write the given inequality in slope-intercept form [tex](y = mx + b)[/tex], let's first isolate the y term:

[tex]-6x + 3y \geq -45[/tex]

Add 6x to both sides:

[tex]3y \geq 6x - 45[/tex]

Now, divide both sides by 3:

[tex]y \geq 2x - 15[/tex]

[tex]\[\begin{align*}\frac{3y}{3} & \geq \frac{6x}{3} - \frac{45}{3} \\y & \geq 2x - 15\end{align*}\][/tex]

Answer:a) Linear: f (x) = 30 + 1.05x

Step-by-step explanation:

Linear: f (x) = 30 + 1.05x is the correct equation.

The answer is option A.

An equation is a mathematical statement this is made up of expressions related with the aid of the same signal. for instance, 3x – five = 16 is an equation. Solving this equation, we get the price of the variable x as x = 7.

A one-step equation is an algebraic equation you may resolve in the most effective one step. You've got solved the equation when you get the variable through itself, and not using numbers in the front of it, on one side of the same signal.

Learn more about the equation here: https://brainly.com/question/1214333

#SPJ2

Answer:

A. right 2, up 3

Step-by-step explanation:

We are asked to find the transformation that occurs from  the graph of [tex]f(x)=x^2[/tex] to [tex]f(x)=(x-2)^2+3[/tex].

Let us recall transformation rules:

[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]

[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]

[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]

[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]

Upon looking at our given functions, we can see that graph of [tex]f(x)=x^2[/tex] is shifted to right by 2 units as 2 is inside parenthesis. The graph is shifted upwards by 3 units as we have positive 3 outside parenthesis.

Therefore, option A is the correct choice.

Both equations start with y =

Set both equations equal to each other and solve for x first:

1/3x-4 = -7/3x +4

Add 7/3x to both sides:

8/3x - 4 = 4

Add 4 to each side:

8/3x = 8

Divide both sides by 8/3

x = 3

Now you have the value of x, replace x in the equation to solve for y:

y = 1/3(3) -4 = 1-4 = -3

y = -7/3(3) +4 = -7+4 = -3

y = -3

X = 3 and y = -3

Answer:

Infinitely Many

Step-by-step explanation:

Equations:

y = 5 - 2x

4x + 2y = 10

There are multiple ways to solve this, but I'm going to use substitution.

Since y = 5 - 2x, I will input this y value into the second equation.

4x + 2(5 - 2x) = 10

From here, it's simple algebra.

4x + 10 - 4x = 10

     - 10         - 10

4x - 4x = 0

0x = 0

Because we essentially have the solution 0 = 0, this means that the system has an infinite amount of solutions.

Why?

Well, they're the same line. (Put both into slope intercept form.)

y = 5 - 2x OR y = -2x + 5

4x + 2y = 10

2y = -4x +10

=                     y = -2x + 5

Answer:

INFINITE  SOLUTIONS.

Step-by-step explanation:

y = 5 - 2x

4x + 2y = 10

From the first equation:

2x + y = 5         Multiply this equation by -2:

-4x - 2y = -10

Adding the above to the second equation:

0 = 0   So the 2 equations are identical and  there are Infinite  SOLUTIONS>

Answer:

I don't possess a graph so I'll teach it to you.

Step-by-step explanation:

In a coordinate plane with 4 quadrants, the formula for this equation is SLOPE. This is fairly a very easy topic to learn about. The formula is y = mx + b.

So I assume you forgot to put the "x" after the 3/4.

Anyway, to answer this the "2" in bthe equation is the y-intercept. So the X-coordinate will ALWAYS be ZERO! O basically you plot at (0,2).

Next, you grab the slope. To get it you must use the RISE OVER RUN technique. You rise 3 UP and since it's a POSITIVE SLOPE, 3/4, NOT -3/4, you RUN 4 units to the RIGHT, which gives you (5,4), I believe. And you keep doing that until the graph is finished. And if you want to go backwards from (0,2), you make the RISE AND RUN, NEGATIVE. It's very simple. In the end you should get a line like "/" on your graph which means it's a POSITIVE SLOPE. If it's "\", IT'S A NEGATIVE SLOPE.

I hope this helps and PLEASE FOLLOW ME! I JUST STARTED BRAINLY!

Answer:

Bethany is correct because consecutive odd integers will each have a difference of two.

For example: [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21...] All those are odd numbers, and have a difference of two.

So every time time we make 'x' an odd number in Bethany's equation, we will get three consecutive numbers.

For example, if 'x' equals '1', then we will get the three consecutive numbers 1, 3 and 5.

If 'x' equals 7, then we will get the three consecutive numbers 7, 9 and 11.

Answer:

A.) Bethany is correct because consecutive odd integers will each have a difference of two

Step-by-step explanation:

The sum of 3 consecutive odd integers is 91. Let the first odd integer is x. The next odd integer will be obtained by adding 2 in x i.e. (x + 2). The third odd integer will be obtained by adding 2 in the second odd integer i.e. (x + 2) + 2 = x + 4

After the information stated we can conclude that:

The 3 odd integers will be:

x  , (x+2) and (x+4)

Their sum is given to be 91. So we can write:

x + (x+2) + (x+4) = 91

Hence, we can conclude that: Bethany is correct because consecutive odd integers will each have a difference of two.

Answer:

Speed = 8mph

Step-by-step explanation:

Speed of wind = 4mph

Let speed of Darrin with no wind be "x" mph

then resultant speed of Darrin, travelling in direction of wind = (x + 4) mph

Using a result, Time = Distance travelled / Net speed

Time taken by Darrin to travel 6miles in direction of wind = 6 / (x + 4)

When Darrin travel in opposite direction of wind, then its net speed                                                  = (x - 4)mph

Darrin travel 2 miles against the wind in 6/(x + 4) hr

then   Distance =  speed ×  time

           2 =  ( x- 4 ) × ( 6/x + 4)

          2x + 8 = 6x - 24

            4x  =  32

              x = 8 mph

Therefore speed of Darrin skateboard with no wind = 8mph

Answer:

Speed without wind will be 8 mph

Step-by-step explanation:

Now by revising basic formula here

Velocity = Distance/Time. . . . (A)

Assume speed without wind is 'x'

When Darrin is moving against wind to cover 2 miles;

net speed will be x-4

When Darrin is moving along with the wind to cover 6 miles;

net speed will be x+4

Please note that the time for covering distance of 2 miles and 6 miles is same,

So, from equation (A)

Time = Distance/Velocity,

Time for 2 miles will be

Time = 2/(x-4)

Time for 6 miles will be

Time = 6/(x+4)

Since, the time for both distances is same, here we can equate,

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

by cross multiply

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

2x+8 = 6x-24

4x = 32

x = 8

So, 8 miles per hour is the speed of Darrin if there is no wind.

Answer:

The correct option is D

Step-by-step explanation:

To find the solution of this problem firstly we will find the probability that some one is in the brass section and play trombone.

We will multiply the probability that a member is in the brass section which is 0.50 with the probability that a member plays trombone, given that he or she is in the brass section which is 0.36

= 0.50 * 0.36

=0.18

Therefore the probability that a randomly selected band member is in the brass section and plays trumpet is 0.18

Thus the correct option is D....

Answer:

D

Step-by-step explanation:

Answer:

2 hours.

Step-by-step explanation:

8 hours x 25 / 100 = 2 hours

Answer:

2 hours.

Step-by-step explanation:

Let the number of hours taken doing paperwork be x.

Shift of each day=8 hours

According to question

x=25%of 8 hours

x=25×8/100

x=2 hours

Thus, answer is 2 hours.

Answer: [tex]15.5\ mm^2[/tex]

Step-by-step explanation:

You can calculate the area of a kite with the following formula:

[tex]A=\frac{d_1d_2 }{2}[/tex]

Where [tex]d_1[/tex] is the length of a diagonal and [tex]d_2[/tex] is the length of the other diagonal.

In this case, you can identify that:

[tex]d_1=6.2\ mm\\d_2=5\ mm[/tex]

Therefore, the final step is to substitute the values into the formula.

Then, the area is:

 [tex]A=\frac{(6.2\ mm)(5\ mm)}{2}\\\\A=15.5\ mm^2[/tex]

Answer:

See below.

Step-by-stepexplanation:

The slope = rise/run

= (7- -5)/(-3-1)

=  12/-4

= -3

In point slope form:

y - y1 = -3(x - x1)

y - (-5) = -3(x - 1)

y + 5 = -3(x - 1) <--------- Point slope form.

y + 5 = -3x + 3

y = -3x - 2. <----------Slope-intercept form.

Answer:

y = -3x - 2

Step-by-step explanation:

If a line passes through (1.-5) and (-3, 7), the appropriate equation for the line in point-slope form is, y = -3x - 2.

Answer:

d

Step-by-step explanation:

Definitely choose the point-slope form y - k = m(x - h) (Answer d)

Final answer:

To write the equation of a line when you have the slope and a single point on the line, the D) point-slope form is the most suitable formula to use.

Explanation:

When you know the slope of a line and a point on the line, the best form to use is the point-slope form. The point-slope formula is expressed as y - y1 = m(x - x1), where m is the slope and (x1, y1) is the known point. This formula allows you to plug in the slope and the coordinates of the point directly to form the equation of the line.

The slope-intercept form y = mx + b is used when you know the slope and the y-intercept, while the point-slope form is specifically designed to formulate an equation given a point and the slope of the line. A horizontal line, which has a slope of zero, nor a vertical line, which has an undefined slope, would not apply to this particular situation.

Answer:

d

Step-by-step explanation:

u got the answer right

Answer:

The process below should work.

Step-by-step explanation:

Let's pretend we have these two points we are trying to find an exponential equation for:  (-2,6) and (2,1).

Exponential equations are of the form [tex]y=a \cdot b^x[/tex] where we must find [tex]a[/tex] and [tex]b[/tex].

So you enter both points into that equation giving you:

[tex]6=a \cdot b^{-2}[/tex]

[tex]1=a \cdot b^{2}[/tex]

I'm going to divide equation 1 by 2 because if I do the a's will cancel and I could solve or b.

[tex]\frac{6}{1}=\frac{a \cdot b^{-2}}{a \cdot b^2}[/tex]

[tex]6=\frac{b^{-2}}{b^2}[/tex]

By law of exponent, I can rewrite the right hand side:

[tex]6=b^{-2-2}[/tex]

[tex]6=b^{-4}[/tex]

Now do ^(-1/4) on both sides to solve for b:

[tex]6^\frac{-1}{4}=b[/tex]

Now we use one of the equations along with our value for b to find a:

[tex]1=a \cdot b^2[/tex] with [tex]b=6^{\frac{-1}{4}}[/tex]

[tex]1=a \cdot (6^{\frac{-1}{4}})^2[/tex]

Simplify using law of exponents:

[tex]1=a \cdot 6^{-\frac{1}{2}}[/tex]

Multiply both sides by 6^(1/2) to solve for a:

[tex]6^{\frac{1}{2}}=a[/tex]

[tex]y=a \cdot b^x[/tex] with [tex]a=6^{\frac{1}{2}} \text{ and } b=6^{\frac{-1}{4}}[/tex] is:

[tex]y=6^\frac{1}{2} \cdot (6^{\frac{-1}{4})^x[/tex]

We can simplify a smidgen:

[tex]y=6^\frac{1}{2} \cdot (6)^\frac{-x}{4}[/tex]

Answer:

8 is the only one that will work

Step-by-step explanation:

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

So this means the x will first be plug into g.

So let's check your choices.

g(6)=1/(6-6)=1/0 so 6 is not in the domain of g which means it isn't in the domain of (f o g).

g(8)=1/(8-6)=1/2  so this is a number so 8 is in the domain of g,

Let's check if 1/2 is in the domain of f.

f(1/2)=sqrt(6*1/2)=sqrt(3) so this is a number so since 1/2 is in the domain of f then 8 is in the domain of (f o g).

g(4)=1/(4-6)=1/(-2)=-1/2 so 4 is in the domain of g,

f(-1/2)=sqrt(6*-1/2)=sqrt(-3) so this is a problem because you can't square root negative numbers so -1/2 isn't in the domain of f, and therefore 4 isn't in the domain of (f o g).

g(2)=1/(2-6)=1/-4=-1/4 so 2 is in the domain of g.

f(-1/4)=sqrt(6*-1/4)=sqrt(-3/2) so again this is a problem because we can't square root negative numbers so -1/4 isn't in the domain of f, and therefore 2 isn't in the domain of (f o g).

Answer: option b

on edg guys:))

Step-by-step explanation:

y ^2/3

Answer:

25,095238095 = 25 2⁄21

Step-by-step explanation:

Just multiply each denominator and numerator straight across and convert to a mixed number, decimal, or whatever you want.

I am joyous to assist you anytime.

Answer:

A and D

Step-by-step explanation:

See I cannot explain you by diagram as I cannot make it here but the short trick is that the angle with the vertex you are looking for should be in the centre.

Here, it is XYZ and ZYX

Answer:

0.1056

Step-by-step explanation:

Given from the question;

Mean=125cm

Standard deviation =12cm

You should find the z* value from  mean and standard deviation

The formula to apply is;

z=(wingspan in question - mean)÷standard deviation

[tex]z=\frac{140-125}{12} =\frac{15}{12} =1.25[/tex]

Using the Z score table read the value of proportion that corresponds to 1.25

From the table, the proportion is 0.1056