2/3 x (-6/7 + 4/5) = (2/3 x 4/5) x (-6/7) : verify

Answer:

Y= 2/3x +(5/3)

Step-by-step explanation:

First, have to get Y alone on one side 3y=2x+5

Second, have to get read of the 3 with the Y so divide each side by three.

Answer:

[tex]y = 2g - 2[/tex]

[tex]y + g = 16[/tex]

Step-by-step explanation:

Given

Let g represent the green marbles

Let y represent the y marbles

Required

Determine the relationship between both marbles

The question says that y is 2 less than twice of g

This implies that: [tex]y = 2g - 2[/tex]

The question further states that, Sarah has a total of 16 marbles;

This implies that [tex]y + g = 16[/tex]

So, the system of equation that defines the relationship between y and g are:

y = 2g - 2

y + g = 16

Answer:

edge 2021

Step-by-step explanation:

If you let g be the variable for the green marbles and y be the variable for the yellow marbles, which equation represents the relationship between yellow and green marbles?

✔ y = 2g - 2

Sarah has a total of 16 marbles. Which equation represents the total number of marbles she has?

✔ y + g = 16

B. [tex]-x^2-2[/tex].

Hope this helps.

Answer:

i think its g(x)=-x^2-2

Step-by-step explanation:

1,3,4 that is the answer

Answer:

Step-by-step explanation:

x³ + 6x² + 5x - 12

A factor of the polynomial is the value of x when substituted into the expression will make it zero

Choosing x + 4

x = - 4

We have

(- 4)³ + 6(- 4)² + 5(- 4) - 12

-64 + 96 - 20 - 12 = 0

Since the result is zero

x + 4 is a factor of the polynomial

Hope this helps you

Answer:

$ 5.65

Step-by-step explanation:

let the cost of a pencil and a ruler be $p and $r respectively.

4p +r= 1 -----(1)

6p +3r= 2.10

divide by 3 throughout:

2p +r= 0.70 -----(2)

Q: 3p +13r= ?

(1) -(2):

(4p +r) -(2p +r)= 1 -0.70

4p +r -2p -r= 0.30 (expand)

2p= 0.30 (simplify)

p= 0.30 ÷2 (÷2 on both sides)

p= 0.15

subst. into (1):

4(0.15) +r= 1

r +0.60= 1

r= 1 -0.60

r= 0.40

cost of three pencils and thirteen rulers

= 3p + 13r

= 3(0.15) + 13(0.40)

= 0.45 + 5.20

= $5.65

Answer:

(3, -3)

Step-by-step explanation:

Given functions:

and

Solution is the Intersect which is found by equalizing the two functions:

Solving for x:

As both values of x for the first function reveal f(x) = -3, the pairs are:

Answer:

30 seconds.

Step-by-step explanation:

So, we have the equation:

[tex]h(t)=-16t^2+h[/tex]

Where t is the time in seconds and h is the initial height.

A barometer falls from a weather balloon at a height of 14,400 feet. In other words, the initial height is 14,400. Substitute for h:

[tex]h(t)=-16t^2+14400[/tex]

We need to find when the barometer hits the ground. Ground level is 0 feet. Therefore, we can substitute h(t) for 0 and solve for the equation (solve for t) in order to find how long (in seconds) it took for the barometer to fall:

[tex]0=-16t^2+14400\\-14400=-16t^2\\900=t^2\\t=\pm\sqrt{900} \\\text{Time cannot be negative.}\\t=\sqrt{900}\\ t=30 \text{ seconds}[/tex]

Therefore, it took 30 seconds for the barometer to hit the ground when it fell at a height of 14,400 feet.

Edit: Spelling.

Answer:

[tex] y = x^2 -5x +6[/tex]

And for this case we want to find the zeros or x interceps r and s so we want to rewrite the function on this way:

[tex] y = (x-r) (x-s)[/tex]

The reason why we have two zeros is because the degree of the polynomial is 2. If we find two numbers that adding we got -5 and multiplied 6 we solve the problem. For this case the solution is r =3, s =2

[tex] y=(x -2)) (x-3)[/tex]

Step-by-step explanation:

For this problem we have the following polynomial given:

[tex] y = x^2 -5x +6[/tex]

And for this case we want to find the zeros or x interceps r and s so we want to rewrite the function on this way:

[tex] y = (x-r) (x-s)[/tex]

The reason why we have two zeros is because the degree of the polynomial is 2. If we find two numbers that adding we got -5 and multiplied 6 we solve the problem. For this case the solution is r =3, s =2

[tex] y=(x -2)) (x-3)[/tex]

Answer:

5 years

Step-by-step explanation:

Firstly, Let's use a function to find how much Jenny owes every year.

Using f(t)=3,000(1.18)^t

We can find the amount of money jenny owes every year.

Now let's try to find how many years it would take her to double her credit card debt.

If we change t=5, we can see that the function gives us an output of 6,863.27 which is double the amount of which she currently owes.

Answer:

[tex]\boxed{85}[/tex]

Step-by-step explanation:

Sum of 38 and -87:

=> 38 + (-87)

=> 38 - 87

=> -49

Subtraction of -134 from -49:

=> -49 - (-134)

=> -49 + 134

=> 85

Answer:

Option C is the correct option.

Step-by-step explanation:

[tex] {36}^{ \frac{1}{2} } [/tex]

Write the number in exponential form with a base of 6

[tex] =( {6}^{2}) \: ^{ \frac{1}{2} } [/tex]

Simplify the expression by multiplying the exponents

[tex] = 6[/tex]

Hope this helps..

Best regards!!

Round this however you need to.

===========================

Work Shown:

Check out the diagram below. We have the following points

Based on those points, we know that

Which allows us to find the distance from C to D. Focus solely on triangle EDC. Use the sine ratio to find x.

sin(angle) = opposite/hypotenuse

sin(angle EDC) = CE/CD

sin(56) = 7130/x

x*sin(56) = 7130

x = 7130/sin(56)

x = 8600.33397283284 approximately

Make sure your calculator is in degree mode.

Answer:

∠AOB and ∠COD are vertical angles

∠DOE and ∠COD are complementary, adjacent

∠AOB and ∠AOD are supplementary, adjacent.

Step-by-step explanation:

Let's start with ∠AOB and ∠COD.

Looking at this, we can see they are the same angles formed by two lines that intersected. These are vertical angles as they are opposite each other.

∠DOE and ∠COD together form the angle ∠EOC, which is a right angle. Complementary angles are any of two that add up to 90°, so these two angles are complementary. They are also adjacent because they are right next to each other.

∠AOB and ∠AOD together form the angle ∠BOD, which has a measure of 180°. Supplementary angles are any of two that add up to 180°, so ∠AOB and ∠AOD are supplementary. They are also adjacent as they are touching/right next to each other.

I hope this helped!

Answer: rotate 180 degrees and reflection across the line y=2

Step-by-step explan

Answer:

Step-by-step explanation:

Answer:

0.872665

Step-by-step explanation:

Answer:

work is shown and pictured

C, infinitely many solutions.

B, one solution.

C, infinitely many solution.

A system of linear equations is a collection of one or more linear equations involving the same variables.

A system of linear equation has

According to the given questions

the given system of equations

(1). 2x+2y=3 and 4x+4y=6

if we see the graph of the above system of linear equations, the graphs are the" exact at same line".

Hence, they have infinitely many solution.

(2). 7x+5y=8 and 7x+7y =8

if we see the graph of the above system of linear equations, the graphs are intersecting at a single point.

Hence, there is only one solution.

(3). -2x+3y=7 and 2x-3y=-7

if we see the graph of the above system of linear equations, the graphs are exact at same line.

Hence, there is infinitely many solutions.

Learn more about the system of linear equations here:https://brainly.in/question/5130012

#SPJ2

Answer:

Step-by-step explanation:

If EG is parallel to the side of the rectangle then lenght of EG is equal to width of rectangle.

If F and H are midpoints of sides of rectangle then FH is parallel to the side of rectangle {wich is perpendicular to the side parallel to EG}. That means the lenght of FH is equal to lenght of rectangle, and FH is perpendicular to EG.

Then FH is sum of hights of triangles EFG and EHG [tex](FH=H_{_{\Delta EFG}}+H_{_{\Delta EHG}})[/tex], and the area of EFGH is sum of areas of triangles EFG and EHG [tex](A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}})[/tex].

So the area of the rectangle:  [tex]\bold{A_{rectangle}=EG\cdot FH}[/tex]

The area of the kite:

                                  [tex]A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}}\\\\A_{kite}=\frac12 EG\cdot H_{_{\Delta EFG}}+\frac12 EG\cdot H_{_{\Delta EHG}}\\\\ A_{kite}=\frac12 EG\cdot (H_{_{\Delta EFG}}+H_{_{\Delta EHG}})\\\\A_{kite}=\frac12 EG\cdot FH\\\\A_{kite}=\frac12 A_{rectangle}[/tex]

No matter the height of the triangles, so no matter the location of the EG

Answer:

g = (h+a) - l

None of them

Step-by-step explanation:

Suppose your car has h liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is g liters. Which of the following expressions always represents how far away the new oil level is from the previous oil level? H+G lGl none of them

Let

h = liters of oil in the morning

l= liters that has leaked

a= liters that were added during the day

g= amount of liters at the end of the evening

Total liters of oil in the evening= (litres of oil in the morning + litres of oil added during the day) - litres of oil that leaked

Substituting each variable into the formula, we have

g = (h+a) - l

Answer:

The domain is all values but x=4 and x=2

Step-by-step explanation:

f(x) = (x+1) / ( x^2-6x+8)

Factor the function

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

The domain of the function is all values of x except where the function does not exist

This is where the denominator goes to zero

(x-4) ( x-2) =0

Using the zero product property

x-4 =0   x-2 =0

x=4   x=2

The domain is all values but x=4 and x=2

Answer:

Hey there!

This, is the graph of your function:

Thus the domain, or all the possible x values would be all real numbers except 2 and 4, because the lines will only reach 2 and 4 when y is infinity.

Hope this helps :)

Answer:

Step-by-step explanation:

A radius to the tangent point always forms a right angle with the tangent.

m∠OAB = m∠OCB = 90°

[tex]m\angle AOC=\stackrel{\big{\frown}}{ADC}=96^o[/tex]

The sum of the angles in the quadrilateral is 360°, so:

x = 360° - 2•90° - 96° = 84°

Answer:

13.2 ft

Step-by-step explanation:

We are given a ladder, a building, and an angle. Let's construct a right triangle (see attachment).

In this right triangle, we know that the hypotenuse (the ladder) is 25 feet, while the angle made between the top of the ladder and the building is 32°. Since we want to find the number of feet between the building and the base of the ladder, we will use the trigonometric function sine, which is opposite divided by hypotenuse.

Here, the opposite side is the value we want to find, while the hypotenuse is the length of the ladder.

We have:

sin(32°) = opposite / hypotenuse = x / 25

x = 25 * sin(32°) ≈ 13.2 ft

The answer is thus 13.2 ft.

~ an aesthetics lover

Answer:

(-5,-28)

Step-by-step explanation:

Use the vertex form y=a(x-h)^2

a=1

h=-5

k=-28

vertex=(h,k)

Answer:  A.  (-5, -28)

Step-by-step explanation:

f(x) = x² + 10x - 3

     a=1    b=10  

The axis of symmetry is the x-coordinate of the vertex:

[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(10)}{2(1)}=-5[/tex]

Input x = -5 into the original equation to find the y-coordinate of the vertex:

f(-5) = (-5)² + 10(-5) - 3

      =  25      -50    -3

      = -28

x, y coordinate of the vertex is: (-5, -28)

Answer:

21

Step-by-step explanation:

since it is a triangle subtract 180 by 137 and 22

180-(137+22) or 180-132-22

hope this helps

Answer:

21

Step-by-step explanation:

We khow that the sum of a triangle's angles sizes is 180°

substract the sum of the two khown angles from 180°

so m<0 = 21°

Answer: a

Step-by-step explanation:

substitute the coordinate values for x and y

y<3x+3, (1,-5)

-5<3(1)+3

-5<3+3

-5<6

the coordinate (1,-5) works, so a is the answer

Answer:

x ∈ R, x ≠ 9

Step-by-step explanation:

Given

f(x) = [tex]\frac{1}{x-9}[/tex]

The denominator of f(x) cannot be zero as this would make f(x) undefined.

To find the value that x cannot be, equate the denominator to zero and solve for x

x - 9 = 0 ⇒ x = 9 ← excluded value

Thus the domain is x ∈ R, x ≠ 9

Answer:

A. 3

Step-by-step explanation:

ΔDEC is bigger than ΔABC by 5. For the hypotenuse, 25 is 5 times bigger than 5.

So, side DE on ΔDEC has to be 5 times bigger than side AB on ΔABC.

If side AB equals 3, side DE equals 18 - 3, which is 15.

15 is five times bigger than 3, so the answer is A. 3.

Hope that helps.

Answer: Choice B

a_n = 10(1/2)^(n-2) is the nth term

average rate of change = -35/3

=======================================================

Explanation:

Each time x increases by 1, y is cut in half. For instance, going from (2,10) to (3,5) shows this.

If we want to go in reverse, decreasing x by 1 will double the y value. So (1,20) is another point and (0,40) is another. We'll be using (0,40) and (3,5) because we want the average rate of change from x = 0 to x = 3. I'm using x in place of n here.

Use the slope formula to find the slope of the line through (0,40) and (3,5)

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

m = (5-40)/(3-0)

m = -35/3

The negative slope means the line goes downhill as you read it from left to right. The average rate of change from n = 0 to n = 3 is -35/3

The nth term of this geometric sequence is 20(1/2)^(n-1) since 20 is the first term (corresponds to n = 1) and 1/2 is the common ratio. Your teacher has done a bit of algebraic manipulation to change the n-1 into n-2. This means the 20 has to change to 10 to counterbalance.

In other words, 20(1/2)^(n-1)  is equivalent to 10(1/2)^(n-2) when n starts at n = 1.

Answer:

The flight speed should be 84.79 miles per hour at angle of 22.92° Northeast

Step-by-step explanation:

The given information are;

The distance from Parrot Point Airport to Ivy Cliffs = 291 miles

The direction from Parrot Point Airport to Ivy Cliffs = 9.1° Northeast

The speed of the wind = 25 miles per hour

The direction of the wind = Southeast

The time for the journey = 3 hours

The component of the wind velocity are;

For Southeast direction which is an inclination of 45°

Speed of the wind = -25 × sin(45) + 25 × cos(45)

Without the wind, the velocity of flight will be V = Displacement/time, which gives;

V = 291/3 = 97 miles/hour = 97 mph

Let the required velocity of flying = X, we have;

X×sin(θ) + X×cos (θ)  -25× sin(45) + 25 × cos(45) = 97×sin(9.1) + 97×cos(9.1)

X×sin(θ) -25× sin(45) = 97×sin(9.1)

X×sin(θ) =  97×sin(9.1 )+25× sin(45 ) = 33.02

X×sin(θ) =  33.02

X×cos (θ) +  25 × cos(45) =  97×cos(9.1)

X×cos (θ) =  97×cos(9.1)-  25 × cos(45) = 78.1

X×cos (θ) =   78.1

∴X×sin(θ)/(X×cos (θ)) = tan(θ) = 33.02/78.1 = 0.423

tan⁻¹(0.423) = 22.918≈ 22.92°

X×sin(θ) =  33.02

X = 33.02/(sin(θ)) = 33.02/(sin(22.92°)) = 84.79 miles per hour

Therefore, the flight speed should be 84.79 miles per hour at angle of 22.92° Northeast.

Answer:

x=46 degrees

Step-by-step explanation:

first find the size of the other angles(let call z and y)

the sum of a straight angle is 180:

180=130+z

z=180-130=50

y=180-96=84

sum of angles of triangle =180

x+y+z=180

50+84+x=180

x=180-134=46 degrees

Answer:

46°

Step-by-step explanation:

Angle of a line = 180°

To find the other side of 130°

The other side = 180° - 130° = 50°

To find the other side of 96°

The other side = 180° - 96° = 84°

To find x°

Total angle of a triangle = 180°

180° = x° + 50° + 84°

x° = 180° - 134°

x° = 46°