The first three steps in determining the solution set of the system of equations algebraically are shown.

y = x2 − x − 3
y = −3x + 5



What are the solutions of this system of equations?

(−2, −1) and (4, 17)
(−2, 11) and (4, −7)
(2, −1) and (−4, 17)
(2, 11) and (−4, −7)

Answer:

[tex]\frac{\sqrt{3} }{4} a^2[/tex]

Step-by-step explanation:

To find the area of an equilateral triangle, we can apply a formula.

[tex]A=\frac{\sqrt{3} }{4} s^2[/tex]

[tex]A= area\\s=side \: length[/tex]

The side length is given a.

Plug a in the formula as the side length.

[tex]A=\frac{\sqrt{3} }{4} a^2[/tex]

Answer:

3 square root over 4 a square

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

f(-9) is the value of f(x) when x = -9. Therefore, f(-9) = 4 from the graph. Doing the same with g(6), we can see that g(6) = 6. Our expression becomes:

-1 * 4 + 7 * 6

= -4 + 42

= 38

Answer:

what expressions?

Step-by-step explanation:

Answer:

Time taken (t) = 2.67 s (Approx)

Step-by-step explanation:

Find:

Time taken (t)

Given:

Initial velocity (u) = 0 m/s

Acceleration due to gravity(a) = -9.8 m/s²

Distance (d) = -35 m

Computation:

Using 2nd equation of motion,

d = ut + (1/2)at²

-35 = (0)t + (1/2)(-9.8)t²

-35 = -4.9 (t²)

t² = 7.1428

t = 2.6726

Time taken (t) = 2.67 s (Approx)

Answer: C

explanation:  a p e x

Explanation:

Start with the template they give, which is y = ax+b. From here, replace 'a' with -2.9 and b with 13.5 to get the answer y = -2.9x + 13.5

The r and r^2 values aren't used to form the regression line. Instead, they are ways to see how good a fit we have. Since r is fairly close to -1, this means we have a really strong negative correlation. All of the points are close or around the same straight line with a negative slope (that slope being -2.9).

Answer:

420

Step-by-step explanation:

To find 63% of 6000, we can do 0.63 * 6000 = 3780 because 63% = 0.63.

1/9th of that is 1/9 * 3780 = 420.

Answer:

420

Step-by-step explanation:

Let's first start by finding 63% of 6000 so we can later find 1/9 of that number.

We can set up a percentage proportion.

[tex]\frac{x}{6000} = \frac{63}{100}[/tex]

[tex]6000\cdot63=378000\\378000\div100 = 3780[/tex]

Now to find 1/9 of 3780.

[tex]\frac{1}{9} \cdot \frac{3780}{1}\\\\\frac{3780}{9} = 420[/tex]

So, the answer is 420.

Hope this helped!

Answer: The area of land =108 m²

Step-by-step explanation:

In the given piece of land is in the shape of a parallelogram.

Diagonals divide it into 2 equal parts.

So, area of parallelogram = 2 x (Area of triangle with sides 12m and 9 m and  15 m)

Heron's formula :

Area of triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\dfrac{a+b+c}{2}[/tex]

Let a= 12 , b= 9 and c = 15

[tex]s=\dfrac{12+9+15}{2}=18[/tex]

Area of triangle = [tex]\sqrt{18(18-12)(18-9)(18-15)}[/tex]

[tex]=\sqrt{18\times6\times9\times3}=\sqrt{2916}=54\ m^2[/tex]

Then, area of parallelogram= 2 x 54 = 108 m²

Hence, the area of land =108 m²

Hi,

[tex]y=5x^{2} +12x-2\\y=x(5x+12)-\frac{46}{5} \\y=5(x+\frac{6}{5} )^{2}-\frac{46}{5} \\[/tex]

Have a good day.

Answer:

33/2

Step-by-step explanation:

6 * 11/4 = 66/4 = 33/2

Answer:

5x-18 this angle is equal to 92

3x+22 this angle is equal to 88

angle a=88

angle b=92

Step-by-step explanation:

set 5x-18 and 3x+22 equal to 180 and solve to get x=22. Now look for ways to fill in a and b. A is an alternate interior angle that will be equal to 3x+22

angle b will be equal to the angle 5x-18

Answer:

The value of x is22°, a is 88° and b is 92°.

Hope it helps..

Answer:

[tex]\overline{DF}[/tex] could be a midsegment of ∠ABC.

Step-by-step explanation:

A midsegment of a triangle must be two things:

1. Parallel to the 3rd side, in this case, [tex]\overline{AD}[/tex].

2. Half the length of the 3rd side, in this case, [tex]\overline{AD}[/tex].

Since we don't know the lengths, we can only go off of 1. There is only one line that is parallel to  [tex]\overline{AD}[/tex] and it is [tex]\overline{DF}[/tex].

Hope this helped!

Answer:

7.5 jars

Step-by-step explanation:

There are 25 students in the art class.

Mr Jones is planning that for the project, each of the 25 students will need 0.3 jar of paint.

The amount of paint Mr Jones needs for this project is therefore the product of the number of students in the class by the amount of paint each student needs.

That is:

25 * 0.3 = 7.5 jars of paint

Mr Jones needs 7.5 jars of paint for the art project.

Answer:

The translation from quadrilateral EFGH to quadrilateral E'F'G'H' is [tex]T_{(2, -4)}[/tex], which is two units to the right (x direction) and 4 units down (negative y direction)

Step-by-step explanation:

The coordinates of quadrilateral EFGH are;

Point E has coordinates (-1, 1)

Point F has coordinates (0, 4)

Point G has coordinates (3, 1)

Point H has coordinates (3, 0)

The coordinates of the translation are;

Point E' has coordinates (0, -3)

Point F' has coordinates (1, 0)

Point G' has coordinates (4, -3)

Point H' has coordinates (4, -4)

The change in the y-coordinate values (y values) are;

From point E to point E', we have;

(-3 - 1) = -4 which is four units down

The change in the x-coordinate values (x values) are;

From point E to point E', we have;

(0 - (-1)) = 2 which is two units to the right

The total change in translation is [tex]T_{(2, -4)}[/tex].

Answer:

30°, 60° and 90°

Step-by-step explanation:

Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.

Note that a right angled triangle is made up of two acute angles and a right angled (90°)

Let's get one of the acute angles first

If Arccos (√3/2)=β

β = cos^-1 √3/2

β = 30°

This shows that one of the acute angles is 30°

To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.

90+30+x = 180

120+x = 180

x = 180-120

x = 60°

All the angle measurement for the right angled triangle are 30°, 60° and 90°

Answer:

volume=3x³+15x²+12x

Step-by-step explanation:

v= l*w*h =(3x )(x+1) (x+4)

v=3x(x²+5x+4)

volume=3x³+15x²+12x

Answer: 3 x minus 3 + 4 = 2 minus x minus 3

              3 x + 1 = negative x minus 1

Step-by-step explanation:

             A and D. Edge 2020

The required equation that Samuel used is 3x -3 + 4 =2- x -3. option A is correct.

Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use, is to be determined.

The equation is the relationship between variables and represented as[tex]y = ax +b[/tex]  is an example of a polynomial equation.

Given equation is [tex]3(x-1) +4 =2 -(x+3)[/tex]
Simplification of the above equation,
opening the parenthesis on both sides
step 1⇒ 3x - 3 + 4 = 2 - x - 3
step 2⇒ 3x + 1 = -x - 1
Transposition of -x to the left side and +1 to the right side
step 4 ⇒ 3x +x = -1 -1
                  4x = -2
Transposition of 4 to the denominator of -2.
step 5⇒ x = -2/4
               x = -1/2

Thus , Step 1 3x -3 + 4 =2- x -3 is the equivalent equation used by the samuel.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ5

hey mate, here is ur answer in the attachment!

Answer:

G(x) = (1 - x)/4

is the inverse function required.

Step-by-step explanation:

Given F(x) = -4x + 1

Let y = F(x)

Then y = -4x + 1

=> y - 1 = -4x

4x = 1 - y

x = (1 - y)/4

That is, the inverse is (1 - x)/4

Therefore, G(x) has to be (1 - x)/4

Answer:

2 - bedroom apartment = 4

3 - bedroom apartment = 2

Step-by-step explanation:

Given the following :

2 - bedroom apartment = $700 / month

3 - bedroom apartment = $900 / month

Last month:

Number of vacant apartment = 6

Amount of Lost rent = $4600

Let a = 2 - bedroom apartment and b = 3 - bedroom apartment

Vacant apartment :

a + b = 6 - - - (1)

Lost rent :

700a + 900b = 4600 - - - (2)

From (1),, a = 6 - b

Substitute a = 6 - b into (2)

700(6 - b) + 900b = 4600

4200 - 700b + 900b = 4600

4200 + 200b = 4600

200b = 4600 - 4200

200b = 400

b = 400/200

b = 2

From (1) ;

a + b = 6

a + 2 = 6

a = 6 - 2

a = 4

a = 2 - bedroom apartment = 4

b = 3 - bedroom apartment = 2

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

Following are the description of the given points:

(a) This is a system of probability, which possibility occurs inside an intended manner whenever they choose this specific point of origin from 1 to 100 with no one reserve the possibility about who gets throughout the survey.  

(b) Its method is different from the random sampling technique with the base available. For example, two individuals whose names identical to both the list have no chance to join within the survey.  

(c) its sample is objective to its everyone can enter the test in equal measure.

Answer:

The value of x is 35

Step-by-step explanation:

In order to calculate the value of x in the  following parallelogram:  2x - 10  

2x + 50, we would have to calculate the following formula:

m<QPS+m<PQR=180°

According to the given data we have the following:

m<QPS=2x - 10  

m<PQR=2x + 50

Therefore, 2x - 10+2x + 50=180

4x+40=180

x=140/4

x=35

━━━━━━━☆☆━━━━━━━

▹ Answer

You can use a graphing calculator. Attached is a picture of it graphed.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

y= [tex]\sqrt{x}[/tex]

Step-by-step explanation:

Answer:

Part 2:

The shape of a banana cut in 45° angle is that of a curve that is closed with the appearance of a flattened circle or an oval similar to an ellipse therefore having two focal points

The drawing of the angle cross section of a cylinder representing the banana is attached

Part 3:

When the banana is cut in half, perpendicular to the base of the banana, the shape formed is circular withe the center of the banana being about the same location as the center of the circle

The drawing of the perpendicular cross section of a cylinder representing the banana is

Step-by-step explanation:

Hey there! I'm happy to help!

When talking about percents, the word "is" usually means equals. Let's use this to solve an equation! We will call our number n. Note that 30% is equal to 0.3 in decimal form because 0.3 is 30% of one! :D

0.3n=45

To solve, we need to isolate the n. To do this, we divide both sides by 0.3 because this cancels out the 0.3 that is being multiplied by n and it shows us what n will then equal.

0.3n÷0.3=45÷0.3

n=150

Therefore, 30% of 150 is 45. Try multiplying 0.3 by 150 and you will get 45!

Have a wonderful day! :D

Answer:

B, C, D

Step-by-step explanation:

if tan theta = 15/8 then the hypotenuse is 17

therefore the correct answers are B, C, D

Answer:

A,C,D

Step-by-step explanation:

When b=0, there is a proportional relationship.

The slope in y=mx+b is the value next to x.

Using RISE/RUN when there is a change of 3 units in x, there is a change of 2 units in y.

Answer:

5/6π.

Step-by-step explanation:

The following data were obtained from the question:

Radius (r) = 12 cm

Area (A) = 60π cm²

Centre angle in radian (∅) =...?

Since we are to look for the centre angle in radian, the area of the sector will be given by:

A = ½r²∅

Inputting the values of the area, A and radius, r, the centre angle, ∅ can be obtained as follow:

A = ½r²∅

60π = ½ × 12² × ∅

60π = ½ × 144 × ∅

60π = 72 × ∅

Divide both side by 72

∅ = 60π/72

∅ = 5/6π

Therefore, the centre angle measured in radian is 5/6π.

Answer:

803.84yd²

Step-by-step explanation:

Surface Area of A Sphere: [tex]A=4\pi r^2[/tex]

We are given the radius of 8 yards.

Using 3.14 for pi:

[tex]A=4*3.14*8^2\\\\A=4*3.14*64\\\\A=12.56*64\\\\\boxed{A=803.84}[/tex]

The correct answer should be 803.84yd².

Brainilest Appreciated.

Answer:

803.84 yd^2

Step-by-step explanation:

4*3.14*8^2

12.56*64

803.84

brainliest pls

hope i helped

           -ZYLYNN